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  • 51.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Dahlquist, ErikMälardalen University, School of Business, Society and Engineering, Future Energy Center.Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Borisenko, OlexandrKiev University, Ukraine.
    Proceedings of the International School “Finance, Insurance, and Energy Markets –       Sustainable Development”2008Conference proceedings (editor) (Refereed)
  • 52.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, Myroslav
    Mälardalen University, Department of Mathematics and Physics.
    Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes with applications to risk theory2006Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    necessary and sufficient condition of weak convergence for first-rara-event times for semi-Markov processes are formulated. Applications to asymptotic analysis of ruin probabilities for risk processes are discussed.

  • 53.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Gyllenberg, Mats
    Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems2008Book (Refereed)
    Abstract [en]

    The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new type of asymptotic expansions for perturbed renewal equation and recurrence algorithms for the constructing of of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomenon in nonlinearly perturbed queuing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area.

  • 54.
    Silvestrov, Dmitrii
    et al.
    School of Education, Culture and Communication, Mälardalen University.
    Gyllenberg, Mats
    Department of Mathematics, University of Helsinki.
    Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems2008 (ed. 1)Book (Other academic)
    Abstract [en]

    This book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented.  Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area.

     

  • 55. Silvestrov, Dmitrii
    et al.
    Jönsson, Henrik
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    Convergence of Option Rewards for Markov Type Price Processes Controlled by Stochastic Indices. 1.Manuscript (Other academic)
  • 56.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Jönsson, Henrik
    Eurandom, Eindhoven University of Technology.
    Stenberg, Fredrik
    School of Education, Culture and Communication, Mälardalen University.
    Convergence of option rewards for Markov type price processes modulated by stochastic indices. II2010In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 80, p. 153-172Article in journal (Refereed)
    Abstract [en]

    A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process modulating the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the pay-off functions are assumed to depend on a perturbation parameter δ ≥ 0 and to converge to the corresponding limit characteristics as δ → 0. In the first part of the paper, asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models were given. In the second part of the paper, these skeleton approximations are used for getting results about the convergence of reward functionals for American type options for perturbed price processes with discrete and continuous time. Examples related to modulated exponential price processes with independent increments are given. 

  • 57.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Jönsson, Henrik
    Eurandom, Eindhoven University of Technology.
    Stenberg, Fredrik
    Nordea Bank, Stockholm, Sweden .
    Convergence of option rewards for Markov type price processes modulated by stochastic indices. II.2010In: Theory of probability and mathematical statistics, ISSN 1547-7363, Vol. 80, p. 153-172Article in journal (Refereed)
  • 58.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Li, Y.
    Stockholm University.
    Lattice Approximation Methods for American Type Options2013Report (Other academic)
  • 59.
    Silvestrov, Dmitrii
    et al.
    Stockholm Univ., Sweden.
    Li, Y.
    Stockholm Univ., Sweden.
    Stochastic Approximation Methods for American Type Options2016In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 6, p. 1607-1631Article in journal (Refereed)
  • 60.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Li, Yanxiong
    Stockholm University, Faculty of Science, Department of Mathematics.
    Stochastic Approximation Methods for American Type Options2016In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 6, p. 1607-1631Article in journal (Refereed)
    Abstract [en]

    Stochastic approximation methods for rewards of American type options are studied. Pay-off functions are non random possibly discontinuous functions or random càdlàg functions. General conditions of convergence for binomial, trinomial, and skeleton reward approximations are formulated. Underlying log-price processes are assumed to be random walks. These processes are approximated by log-price processes given by random walks with discrete distributions of jumps. Backward recurrence algorithms for computing of reward functions for approximating log-price processes are given. These approximation algorithms and their rates of convergence are numerically tested for log-price processes represented byGaussian and compoundGaussian random walks. Comparison of the above approximation methods is made.

  • 61.
    Silvestrov, Dmitrii
    et al.
    Stockholm University.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Convergence of option rewards for multivariate price processes2013In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 85, p. 53p. 115-131Article in journal (Refereed)
    Abstract [en]

    American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes.Convergence results areobtained for optimal reward functionals of American type options forperturbed multivariate Markov processes. Theseresults are applied to approximation tree type algorithms forAmerican type options for exponential diffusion type price processes.Application to mean-reverse price processes used to model stochasticdynamics of energy prices are presented. Also application to reselling of European options are given.

  • 62.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lundgren, Robin
    School of Education, Culture and Communication, Mälardalen University.
    Optimal Stopping and Reselling of European Options2010In: Mathematical and Statistical Methods in Reliability Applications to Medicine, Finance,  and Quality Control: Applications to Medicine, Finance,  and Quality Control / [ed] V. Rykov, N. Balakrishnan, M. Nikulin, Boston: Birkhäuser , 2010, p. 378-394Chapter in book (Other academic)
    Abstract [en]

    The problem of optimal reselling of European options is studied. A bivariate exponential diffusion process is used to describe the reselling model. In this way, the reselling problem is imbedded to the model of finding optimal reward for American type option based on this process. Convergence results are formulated for optimal reward functionals of American type options for perturbed multi-variate Markov processes. An approximation bivariate tree model is constructed and convergence of optimal expected reward for this tree model to the optimal expected reward for the corresponding reselling model is proved. 

  • 63.
    Silvestrov, Dmitrii
    et al.
    School of Education Culture and Communication, Mälardalen University.
    Lundgren, Robin
    School of Education, Culture and Communication, Mälardalen University.
    Kukush, Alexander
    Department of Mathematical Analysis, Kiev University.
    Reselling of options and convergence of option rewards2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 1(96), p. 149-172Article in journal (Refereed)
    Abstract [en]

    The problem of optimal reselling of European options is studies. A bivariate exponential diffusion process is used to describe the reselling model. In this way, the reselling problem is imbedded to the model of finding optimal reward for American type option based on this process. Convergence results are obtained for optimal reward functionals of American type options for perturbed multivariate Markov processes. An approximation bivariate tree model is constructed and convergence of optimal expected reward for this tree model to the optimal expected reward for the corresponding American type option is proved.

     

  • 64.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    The analytical finance package2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13 (29), no 4, p. 201-209Article in journal (Refereed)
    Abstract [en]

    We describe the Analytical Finance Package, a set of Java applets which is developing at the Mälardalen University.

  • 65.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Manca, Raimondo
    University La Sapienza, Italy.
    Recurrent Algorithms for Mixed Power-Exponential Moments of Hitting Times for Semi-Markov Processes2017In: Proceedings of the 17th Applied Stochastic Models and Data Analysis International Conference with the 6th Demographics Workshop / [ed] Christos H. Skiadas, International Society for the Advancement of Science and Technology , 2017, p. 919-937Conference paper (Refereed)
    Abstract [en]

    New algorithms for computing exponential and mixed power-exponential moments of hitting times and accumulated rewards of hitting type for semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations connecting exponential moments of rewards.

  • 66.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Manca, Raimondo
    Reward Algorithms for Semi-Markov Processes2017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1191-1209Article in journal (Refereed)
    Abstract [en]

    New algorithms for computing power moments of hitting times and accumulated rewards of hitting type for semi-Markov processes are developed. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations connecting moments of rewards. Applications are discussed as well as possible generalizations of presented results and examples.

  • 67.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Manca, Raimondo
    Rewards algorithms for exponential moments of hitting times for semi-Markov processes2016Report (Other academic)
    Abstract [en]

    New algorithms for computing exponential moments of hitting times and accumulated rewards of hitting type for semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations connecting exponential moments of rewards. Applications are discussed as well as possible generalizations of presented results and examples

  • 68.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Manca, Raimondo
    University of Rome "La Sapienza".
    Silvestrova, Evelina
    Mälardalen University.
    Computational Algorithms for Moments of Accumulated Markov and Semi-Markov Rewards:  2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 7, p. 1453-1469Article in journal (Refereed)
    Abstract [en]

    Power moments for accumulated rewards defined on Markov and semi-Markov chains are studied. A model with mixed timespace termination of reward accumulation is considered for inhomogeneous in time rewards and Markov chains. Characterization of power moments as minimal solutions of recurrence system of linear equations, sufficient conditions for finiteness of these moments and upper bounds for them, expressed in terms of so-called test functions, are given. Backward recurrence algorithms for funding of power moments of accumulated rewards and various time-space truncation approximations reducing dimension of the corresponding recurrence relations are described. Applications to finding of moments for accumulated rewards for complex insurance contracts are presented as well as results of numerical experimental studies.

  • 69.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Martin-Löf, AndersStockholm University, Faculty of Science, Department of Mathematics.
    Modern Problems in Insurance Mathematics2014Collection (editor) (Refereed)
    Abstract [en]

    The boook is a compilation of 21 of the papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University 0n 11-14 June, 2013. 

  • 70.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Martin-Löf, AndersStockholm University, Sweden.
    Modern Problems in Insurance Mathematics2014Conference proceedings (editor) (Refereed)
  • 71.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Petersson, M.
    Stockholm University.
    Asymptotic Expansions for Perturbed Discrete Time Renewal Equations and Regenerative Processes2012Report (Other academic)
  • 72.
    Silvestrov, Dmitrii
    et al.
    Stockholm University.
    Petersson, M.
    Stockholm University.
    Exponential expansions for perturbed discrete time renewal equations2013In: Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference / [ed] A.Karagrigoriou, A. Lisnianski, A. Kleyner, I. Frenkel, John Wiley & Sons, 2013, p. 349-362Chapter in book (Refereed)
  • 73.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Petersson, Mikael
    Stockholm University, Faculty of Science, Department of Mathematics.
    Exponential Expansions for Perturbed Discrete Time Renewal Equations2013In: Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference / [ed] Ilia B. Frenkel, Alex Karagrigoriou, Anatoly Lisnianski, Andre Kleyner, Chichester: John Wiley & Sons, 2013, p. 349-362Chapter in book (Refereed)
    Abstract [en]

    This chapter presents results about the asymptotic behavior of the solution x(φ)(n) of a perturbed discrete time renewal equation as φ--> 0 and n-->? simultaneously. It consider two cases of so-called quasi-stationary and pseudo-stationary asymptotics, where the limiting distribution f (0)(k) may be, respectively, improper or proper. The author improves the asymptotic relation to the much more advanced form of an exponential asymptotic expansion. The chapter illustrates theoretical results by examples related to queuing systems and risk processes. It briefly shows the way of getting the renewal equation. It repeats the method of finding a similar continuous time renewal equation for ruin probabilities, given, for example in Feller (1966) and Grandell (1991).

  • 74.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Petersson, Mikael
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hössjer, Ola
    Stockholm University, Faculty of Science, Department of Mathematics.
    Nonlinearly perturbed birth-death-type models2016Report (Other academic)
    Abstract [en]

    Asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models are presented. Applications to models of population growth, epidemic spread and population genetics are discussed.

  • 75.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Petersson, Mikael
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hössjer, Ola
    Stockholm University, Faculty of Science, Department of Mathematics.
    Nonlinearly perturbed birth-death-type models2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4–6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer , 2018, p. 189-244Chapter in book (Refereed)
    Abstract [en]

    Asymptotic expansions are presented for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models, as well as algorithms for computing the coefficients of these expansions. Three types of applications are discussed in detail. The first is a model of population growth, where either an isolated population is perturbed by immigration, or a sink population with immigration is perturbed by internal births. The second application is epidemic spread of disease, in which a closed population is perturbed by infected individuals from outside. The third model captures the time dynamics of the genetic composition of a population with genetic drift and selection, that is perturbed by various mutation scenarios.

  • 76.
    Silvestrov, Dmitrii S.
    Stockholm University, Faculty of Science, Department of Mathematics.
    American-Type Options: Stochastic Approximation Methods, Volume 12014Book (Refereed)
    Abstract [en]

    The book gives a systematical presentation of stochastic approximation methods for models of American type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. It is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies. 

  • 77.
    Silvestrov, Dmitrii S.
    Stockholm University, Faculty of Science, Department of Mathematics.
    American-type options: stochastic approximation methods, volume 22014Book (Refereed)
    Abstract [en]

    The book gives a systematical presentation of stochastic approximation methods for models of American type options with general pay-off functions for continuous time Markov log-price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov log-price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also presents results of experimental studies and contains an extended bibliography of works in the area. It is the first volume of the comprehensive two volumes monograph. It is the second volume of the comprehensive  two-volume monograph. The first volume presents stochastic approximation methods for American-type options with general pay-off functions for discrete time modulated Markov log-price processes. 

  • 78.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Upper bounds for exponential moments of hitting times for semi-Markov processes2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 533-543Article in journal (Other academic)
    Abstract [en]

    Necessary and sufficient conditions for the existence of exponential moments for hitting times for semi-Markov processes are found. These conditions and the corresponding upper bounds for exponential moments are given in terms of test-functions. Applications to hitting times for semi-Markov random walks and queuing systems illustrate the results.

  • 79.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Upper bounds for exponential moments of hitting times for semi-Markov processes2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 533-544Article in journal (Refereed)
    Abstract [en]

    Necessary and sufficient conditions for the existence of exponential moments for hitting times for semi-Markov processes are found. These conditions and the corresponding upper bounds for exponential moments are given in terms of test-functions. Applications to hitting times forsemi-Markov random walks and queuing systems illustrate the results.

  • 80.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, M.O.
    Mälardalen University, Department of Mathematics and Physics.
    Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. I2006In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 151-186Article in journal (Refereed)
    Abstract [en]

    necessary and sufficient conditions for weak convergence of first-rare-event time for semi-Markov processes are given

  • 81.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, M.O.
    Mälardalen University, Department of Mathematics and Physics.
    Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. II2006In: Theory of Stochstic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 187-202Article in journal (Refereed)
    Abstract [en]

    Necessary and sufficient condition for weak convergence of stochastic flows of first-rare-event times controlled by semi-Markov processes are given. Also necessary and sufficient conditions for diffusion and stable approximations of ruin probabilities for risk processes are given.

  • 82.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jönsson, Henrik
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander G.
    Kiev University, Ukraine.
    Optimal stopping strategies for American type options2004Conference paper (Other academic)
  • 83.
    Silvestrov, Dmitrii S.
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lundgren, Robin
    Convergence of option rewards for multivariate price processes2012In: Theory of probability and mathematical statistics, ISSN 1547-7363, Vol. 85, p. 115-131Article in journal (Refereed)
    Abstract [en]

    American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes. Convergence results for optimal reward functionals of American type options for perturbed multivariate Markov processes are presented. These results are applied to approximation tree type algorithms for American type options for exponential multivariate Brownian price processes and mean-reverse price processes used to model stochastic dynamics of energy prices.

  • 84.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrova, Evelina
    Mälardalen University, Department of Mathematics and Physics.
    Stochastic modelling of insurance business with dynamical control of investments2004In: 3rd Conference in Actuarial Science & Finance in Samos, Karlovassi, September 2-5 2004, 2004, p. page 54-Conference paper (Other academic)
  • 85.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Mishura, Yu.S.
    Mälardalen University, Department of Mathematics and Physics.
    Limit theorems for stochastic Riemann-Stieltjes integrals2004In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 10(26), p. 122-140Article in journal (Refereed)
  • 86.
    Silvestrov, Dmitrii S.
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei D.
    Asymptotic Expansions for Power-Exponential Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes2017In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 171-187Article in journal (Refereed)
    Abstract [en]

    New algorithms for construction of asymptotic expansions for exponential and power-exponential moments of hitting times for  nonlinearly perturbed  semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and the systematical use  of operational calculus for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of a phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.

  • 87.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrova, Evelina
    Mälardalen University, Department of Mathematics and Physics.
    Master programmes in analytical finance at Mälardalen University2004Conference paper (Other academic)
  • 88.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    Pricing process with stochastic volatility controlled by a semi-Markov process in option pricing2004Conference paper (Other academic)
  • 89.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef
    Katholieke Universiteit Leuven, Belgium..
    Limit theorems for mixed max-sum processes with renewal stopping2004Conference paper (Other academic)
  • 90.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef L.
    Katholieke Universiteit Leuven, Belgium.
    Limit theorems for mixed max-sum processes with renewal stopping2004In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 14, no 4, p. 1838-1868Article in journal (Refereed)
    Abstract [en]

    This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theoremsof weak convergence type are obtained as well as functional limit theorems.

  • 91.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Yadrenko, M.I.
    Mälardalen University, Department of Mathematics and Physics.
    Zinchenko, N.M.
    Mälardalen University, Department of Mathematics and Physics.
    Improvement of economic-statistical education in Ukraine and TEMPUS Networking project 22012-2001 (In: Proceedings of the Eighth International2004In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 10, no 26, p. 162-171Article in journal (Refereed)
  • 92.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Yadrenko, Mikhailo
    Mälardalen University, Department of Mathematics and Physics.
    Zinchenko, Nadiia
    Mälardalen University, Department of Mathematics and Physics.
    Improvement of economic-statistical education in Ukraine and Tempus Networking project 22012-20012004Conference paper (Other academic)
  • 93.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Sergienko, V.Kovalchuk, Yuriy
    Proceedings of the International Summer School “Educational Measurements: Teaching, Research, and Practice”2010Conference proceedings (editor) (Refereed)
  • 94.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Asymptotic Expansions for Power-Exponential Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes2017Report (Other academic)
    Abstract [en]

    New algorithms for computing asymptotic expansions for exponential and mixed power-exponential moments of hitting times for non-linearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and some kind of operational calculus for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have a universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of the phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.

  • 95.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic expansions for power-exponential moments of hitting times for nonlinearly perturbed semi-Markov processes2017In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 171-187Article in journal (Refereed)
    Abstract [en]

    New algorithms for construction of asymptotic expansions for exponential and power-exponential moments of hitting times for nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and the systematical use of operational calculus for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of a phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.

  • 96.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Asymptotic expansions for stationary and quasi-stationary distributions of perturbed semi-Markov processes2016In: ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences / [ed] Seenith Sivasundaram, New York: American Institute of Physics (AIP), 2016, Vol. 1, p. 1-9, article id 020147Conference paper (Refereed)
    Abstract [en]

    New algorithms for computing asymptotic expansions, without and with explicit upper bounds for remainders, for stationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to models with an arbitrary asymptotic communicative structure of phase spaces.

  • 97.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic expansions for stationary and quasi-stationary distributions of perturbed semi-Markov processes2017In: AIP Conference Proceedings / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020147-1-020147-9, article id 020147Conference paper (Refereed)
    Abstract [en]

    New algorithms for computing asymptotic expansions, without and with explicit upper bounds for remainders, for stationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to models with an arbitrary asymptotic communicative structure of phase spaces. 

  • 98.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 12019In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 945-964Article in journal (Refereed)
    Abstract [en]

    New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders.

  • 99.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Mälardalen University, Sweden.
    Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 12019In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 945-964Article in journal (Refereed)
    Abstract [en]

    New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders.

  • 100.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 22019In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 965-984Article in journal (Refereed)
    Abstract [en]

    Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of sequen- tial phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. 

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