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  • 1.
    Abola, Benard
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mango, John
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Nonlinearly  Perturbed Markov Chains  and  Information Networks2019Inngår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, s. 51-79Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding  a special damping matrix multiplied by a small damping (perturbation) parameter ε. In this paper, we present results of the detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

  • 2. Biffi, Elena
    et al.
    D'Amico, Guillermo
    Di Biase, G
    Janssen, J
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules II2008Inngår i: Journal of Numerical and Applied Mathematics, Vol. 96, s. 59-86Artikkel i tidsskrift (Fagfellevurdert)
  • 3. Biffi, Elena
    et al.
    D'Amigo, Guillermo
    Di Biase, Giuseppe
    Janssen, Jacques
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules. I.2008Inngår i: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 1, s. 28-58Artikkel i tidsskrift (Fagfellevurdert)
  • 4.
    Drozdenko, M.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrov, D.
    Mälardalens högskola, Institutionen för matematik och fysik.
    On necessary and sufficient conditions for approximations of ruin probabilities2004Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Necessary and sufficient condition for diffusion and stable approximation of ruin probabilities for risk processes are formulated

  • 5.
    Ekheden, Erhard
    et al.
    Stockholm University.
    Silvestrov, Dmitrii
    Stockholm University.
    Coupling and explicit rates of convergence in Cramér-Lundberg approximation for          reinsurance risk processes2011Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, nr 19-20, s. 3524-3539Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A classical result in risk theory is the Cramér-Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramér-Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e.g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

  • 6.
    Ekheden, Erland
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Coupling and Explicit Rate of Convergence in Cramer-Lundberg Approximation for Reinsurance Risk Processes2011Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, nr 19-20, s. 3524-3539Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A classical result in risk theory is the Cramer-Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramer-Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e. g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

  • 7.
    Jönsson, H.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, A.G.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrov, D.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Supplement to the paper "Threshold structure of optimal stopping domains for American type options": Theory of Stochastic Processes, v. 8(24), no. 1-2 (2002), 170-1772004Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    Conditions, which provide a one-threshold structure for optimal stopping strategies for American type options, are given.

  • 8.
    Jönsson, Henrik
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Domains for American Type Options2002Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 8, nr 1-2, s. 169-176Artikkel i tidsskrift (Annet vitenskapelig)
  • 9.
    Jönsson, Henrik
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Strategies for American Type Option. I2004Inngår i: Theory of Probability and Mathematical Statistics, ISSN 1547-7363, Vol. 71, s. 82-92Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper presents results of theoretical studies of optimal stopping domains of American type options in discrete time. Sufficient conditions on the payoff functions and the price process for the optimal stopping domains to have one-threshold structure are given. We consider monotone, convex and inhomogeneous-in-time payoff functions. The underlying asset's price is modelled by an inhomogeneous discrete time Markov process.

  • 10.
    Jönsson, Henrik
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, Alexander
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrov, Dmitrii
    Mälardalens högskola, Institutionen för matematik och fysik.
    Threshold structure of optimal stopping strategies for American type options2004Rapport (Annet vitenskapelig)
  • 11.
    Jönsson, Henrik
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Strategies for American Type Options. II2005Inngår i: Theory of Probability and Mathematical Statistics, ISSN 1547-7363, Vol. 72, s. 42-53Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper presents results of theoretical studies of optimal stopping domains of American type options in discrete time. Sufficient conditions on the payoff functions and the price process for the optimal stopping domains to have one-threshold structure are given. We consider monotone, convex and inhomogeneous-in-time payoff functions. The underlying asset's price is modelled by an inhomogeneous discrete time Markov process.

  • 12.
    Jönsson, Jönsson
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Kukush, A.G.
    Kiev University, Ukraine.
    Silvestrov, D.S.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Optimal stopping strategies for American type options2004Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    New results on a multi-theshold structure of optimal stopping strategies for American type options for Markov type price processes are presented.

  • 13.
    Kukush, Alexander G.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrov, Dmitrii S.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Optimal pricing of American type options with discrete time2004Inngår i: Theory of Stochastic Processes, Vol. 10, nr 26, s. 72-96Artikkel i tidsskrift (Fagfellevurdert)
  • 14.
    Lundgren, Robin
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Convergence and Approximation of Option Rewards for Multivariate Price Processes2009Rapport (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    Multivariate Markov price processes and American type options for such processes with generalpayoff functions with not more than polynomial rate of growth are considered. Convergence results are obtainedfor optimal reward functionals of American type options for perturbed multivariateMarkov processes and payoff functions. These results are applied to approximation tree type algorithmsfor American type options for exponential diffusion type priceprocesses including mean-reverse stochastic processesused to model stochastic dynamics of energy prices.

  • 15. Lundgren, Robin
    et al.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Convergence of option rewards for multivariate price processes2009Rapport (Annet vitenskapelig)
    Abstract [en]

    American type options with general payoff functions with not more than polynomial rate of growth are considered for multivariate Markov price processes. Convergence results are obtained for optimal reward functionals of American type options for perturbed multivariate Markov processes. These results are applied to approximation tree type algorithms for American type options for exponential diffusion type price processes. Applications to mean-reverse stochastic processes used to model stochastic dynamics of energy prices are presented. Also applications to reselling of European options are given.

  • 16.
    Lundgren, Robin
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Optimal stopping and reselling of European options2010Inngår i: Mathematical and Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishan, N., Nikulin, M, Boston: Birkhäuser , 2010Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    We consider the problem of optimal reselling of European options. 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. 

  • 17.
    Lundgren, Robin
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Kukush, Alexander
    Kiev University.
    Reselling of options and convergence of option rewards2008Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 30, nr 3-4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the problem of optimal reselling of Europeanoptions. A bivariate exponential diffusion process is used todescribe the reselling model. In this way, the reselling problem isimbedded to the model of finding optimal reward for American typeoption based on this process. Convergence results are obtained foroptimal reward functionals of American type options for perturbedmulti-variate Markov processes. An approximation  bivariate treemodel is constructed and convergence of optimal expected reward forthis tree model to the optimal expected reward for the correspondingAmerican type option is proved

  • 18.
    Malyarenko, Anatoliy
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrov, Dmitrii S.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Silvestrova, Evelina
    Mälardalens högskola, Institutionen för matematik och fysik.
    Stochastic modelling of insurance business with dynamical control of investments2004Inngår i: 6th World Congress of Bernoulli Society for Mathematical Statistics and Probability, Barcelona, July 26--31 2004, 2004, s. page 181-Konferansepaper (Annet vitenskapelig)
  • 19.
    Manca, R.
    et al.
    Universit´a di Roma La Sapienza, Italy.
    Silvestrov, Dmitrii
    Mälardalens högskola, Institutionen för matematik och fysik.
    Stenberg, Fredrik
    Mälardalens högskola, Institutionen för matematik och fysik.
    Homogeneous backward semi-Markov reward models for insurance contracts2005Inngår i: Proceedings of ASMDA 2005 Conference: Brest, 2005, 2005, s. 959-967Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Numerical algorithms for eveluation of higher order moments for semi-Markov rewards processes are presented. Results of numerical experiments are given and commented.

  • 20.
    Ni, Ying
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Malyarenko, Anatoliy
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbations2008Inngår i: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, nr 1, s. 173-197Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The model of nonlinearly perturbedcontinuous-time renewal equation is studied in this paper.The perturbation conditions considered involve asymptoticalexpansions with respect to asymptotic scale$\{\varphi_{n,m}(\varepsilon) = \varepsilon^{n +m\omega}\}$,with $n, m$ being non-negative integers and $\omega >1$ beingirrational number. Such asymptotical scale results in non-polynomialtype of asymptotic expansions for solutions for perturbed renewalequations. An example of risk processes with perturbations describedabove and asymptotic expansions in diffusion approximation for ruinprobabilities in this model are given.

  • 21.
    Silvestrov, D.
    Mälardalens högskola, Institutionen för matematik och fysik.
    About my teacher2005Inngår i: In World of Mathematics, Vol. 11, nr 1, s. 33-37Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    A memorial notes about my teacher, Professor Mikhail Yadrenko, our joint work, cooperation, and friendship.

  • 22.
    Silvestrov, D.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Quasi-stationary phenomena in nonlinearly perturbed stochstic systems2006Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    New method of asymptotic analysis for nonlinearly perturbed stochastic processes and systems are presented. Applications to queuing systems, population dynamics systems, and risk processes are described

  • 23.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Borisenko, O.
    Proceedings of the International Summer School “Insurance and Finance: Science, Practice and Education”: Foros, 20062006Konferanseproceedings (Fagfellevurdert)
  • 24.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Borisenko, O.Kiev University, Ukraine.
    Proceedings of the International Summer School “Insurance and Finance: Science, Practice and Education": Foros, 20072007Konferanseproceedings (Fagfellevurdert)
  • 25.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Drozdenko, M.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Necessary and Sufficient Conditions for Weak Convergence of First-Rare-Event Times for Semi-Markov Processes with Applications to Risk Theory2005Rapport (Annet vitenskapelig)
    Abstract [en]

    Necessary and sufficient conditions for weak convergence of first-rare-event times and stochastic flows of first-rare-events for semi-Markov processes are obtained. Also necessary and sufficient conditions for diffusion and stable approximations for ruin probabilities for riosk processes age given.

  • 26.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Jonsson, H.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Stenberg, F.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Convergence of option rewards for Markov type price processes2007Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), nr 4, s. 189-200Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    General condition of convergence are given for optimal rewards of American type options for perturbed Markopv type price processes controlled by market stochastic indices

  • 27.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Jönsson, H.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Stanberg, F.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Convergence of Option Rewards for Markov Type Price Processes Controlled by Stochastic Indicies. 12006Rapport (Annet vitenskapelig)
    Abstract [en]

    Conditions of convergence for optimal expected rewards of American type options are given for perturbed Markov type price processes controlled by stochstic indices

  • 28.
    Silvestrov, D.
    et al.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Teugels, J.
    Masol, V.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Malyarenko, A.
    Mälardalens högskola, Institutionen för matematik och fysik.
    Reinsurance analyser2006Inngår i: International Conference Modern Stochastics: Theory and Applications, Kiev, June 19--23, 2006: abstract of communication, 2006, s. page 245-Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    A program system for analysis and comparison of reincurance contracts is presented.

  • 29.
    Silvestrov, Dimitrii
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Silvestrov, Sergei
    Nonlinearly Perturbed Semi-Markov Processes2017Bok (Fagfellevurdert)
    Abstract [en]

    The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come. 

  • 30.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A journey in the word of stochastic processes2018Inngår i: Stochastic processes and applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer, 2018, s. 7-21Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This paper presents a survey of research results obtained by the authorand his collaborators in the areas of limit theorems for Markov-type processes andrandomly stopped stochastic processes, renewal theory and ergodic theorems forperturbed stochastic processes, quasi-stationary distributions for perturbed stochas-tic systems, methods of stochastic approximation for price processes, asymptoticexpansions for nonlinearly perturbed semi-Markov processes and applications ofthe above results to queuing systems, reliability models, stochastic networks, bio-stochastic systems, perturbed risk processes, and American-type options.

  • 31.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A Journey in the World of Stochastic Processes2017Rapport (Annet vitenskapelig)
    Abstract [en]

    This paper presents a survey of research results obtained by the author and his collaborators in the areas of limit theorems for Markov-type processes and randomly stopped stochastic processes, renewal theory and ergodic theorems for perturbed stochastic processes, quasi-stationary distributions for perturbed stochastic systems, methods of stochastic approximation for price processes, asymptotic expansions for nonlinearly perturbed semi-Markov processes  and applications of the above results to queuing systems, reliability models, stochastic networks, bio-stochastic systems, perturbed risk processes, and American-type options.

  • 32.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Algorithms of Phase Space Reduction and Asymptotics of Hitting Times for Perturbed Semi-Markov Processes2019Rapport (Annet vitenskapelig)
    Abstract [en]

    The report presents new asymptotic recurrent algorithms of phase space reduction for singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence of expectations for hitting times as well as recurrent formulas for computing the corresponding normalisation functions, Laplace transforms for limiting distributions and limits for expectations.

  • 33.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
    American-Type Options, Stochastic Approximation Methods, Volume 22015Bok (Fagfellevurdert)
  • 34.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
    American-Type Options:  Stochastic Approximation Methods. Volume I2014Bok (Fagfellevurdert)
  • 35.
    Silvestrov, Dmitrii
    Mälardalens högskola, Institutionen för matematik och fysik.
    Asymptotic expansions for distributions of the surplus prior and at the time of ruin2007Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), nr 4, s. 183-188Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Exponential asymptotic expansion for distributions of the surplus prior and at the time of ruin are given for perturbed risk processes

  • 36.
    Silvestrov, Dmitrii
    Mälardalens högskola, Institutionen för matematik och fysik.
    Asymptotic expansions for quasi-stationary distributions of nonlinearly perturbed semi-Markov processes2007Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), nr 1-2, s. 267-271Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Asymptotic expansions for quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are given

  • 37.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Convergence in Skorokhod J-topology for compositions of stochastic processes2008Inngår i: Theory Stoch. Process., ISSN 0321-3900, Vol. 14, nr 1, s. 126-143Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A survey on functional limit theorems for compositions of stochastic processes ispresented. Applications to stochastic processes with random scaling of time, randomsums, extremes with random sample size, generalised exceeding processes, sum- andmax-processes with renewal stopping, and shock processes are discussed.

  • 38.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Improved Asymptotics for Ruin Probabilities2014Inngår i: Modern Problems in Insurance Mathematics / [ed] Dimitrii Silvestrov, Anders Martin-Löf, Springer, 2014, s. 37-68Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This paper presents a survey of results on improved asymptotics for ruin probabilities in the Cramér-Lundberg, diffusion, and stable approximations of ruin probabilities for perturbed risk processes, obtained by the author and his collaborators. These results are: exponential asymptotic expansions for ruin probabilities in the Cramér-Lundberg anddiffusion approximations of ruin probabilities; necessary and sufficient conditions for convergence of ruin probabilities in the model of diffusion and stable approximations; and explicit exponential rates of convergence in the Cramér-Lundberg approximation for ruin probabilities for reinsurance risk processes.

  • 39.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
    Improved Asymptotics for Ruin Probabilities2014Inngår i: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, s. 37-68Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This chapter presents a survey of results on improved asymptotics for ruin probabilities in the Cramér–Lundberg, diffusion, and stable approximations of ruin probabilities for perturbed risk processes, obtained by the author and his collaborators. These results are: exponential asymptotic expansions for ruin probabilities in the Cramér–Lundberg and diffusion approximations of ruin probabilities; necessary and sufficient conditions for convergence of ruin probabilities in the model of diffusion and stable approximations; and explicit exponential rates of convergence in the Cramér–Lundberg approximation for ruin probabilities for reinsurance risk processes.

  • 40.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Individual ergodic theorem for perturbed alternating regenerative processes2018Inngår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer , 2018, s. 23-89Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    The paper presents results of complete analysis and classification of individual ergodic theorems for perturbed alternating regenerative processes with semi-Markov modulation. New short, long and super-long time ergodic theorems for regularly and singular type perturbed alternating regenerative processes are presented.

  • 41.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Necessary and sufficient conditions for convergence of first-rare-event times for perturbed semi-Markov processes2016Rapport (Annet vitenskapelig)
    Abstract [en]

    Necessary and sufficient conditions for convergence in distribution of first-rare-event times and convergence in Skorokhod J-topology of first-rare-event-time processes for perturbed semi-Markov processes with finite phase space are obtained.

  • 42.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes2016Inngår i: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 95, s. 119-137Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Necessary and sufficient conditions for convergence in distribution offirst-rare-event times and convergence in Skorokhod J-topology of first-rare-event-time processes for perturbed semi-Markov processes with finite phase space are obtained.

  • 43.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Nonlinearly perturbed stochastic processes2008Inngår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 14, nr 3-4, s. 129-164Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper is a survey of results presented in the recent book [25]1) .This book is devoted to studies of quasi-stationary phenomena innonlinearly perturbed stochastic systems. New methods of asymptoticanalysis for nonlinearly perturbed stochastic processes basedon new types of asymptotic expansions for perturbed renewal equationand recurrence algorithms for construction of asymptotic expansionsfor Markov type processes with absorption are presented.Asymptotic expansions are given in mixed ergodic (for processes) andlarge deviation theorems (for absorption times) for nonlinearly perturbedregenerative processes, semi-Markov processes, and Markovchains. Applications to analysis of quasi-stationary phenomena innonlinearly perturbed queueing systems, population dynamics andepidemic models, and risk processes are presented. The book alsocontains an extended bibliography of works in the area.

  • 44.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Nonlinearly perturbed stochastic processes and systems2011Inngår i: Mathematical and  Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishnan, N., Nikulin, M., Boston: Birkhäuser Verlag, 2011, s. 19-34Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    The paper is a survey of the latest results on 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. 

  • 45.
    Silvestrov, Dmitrii
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Nonlinearly Perturbed Stochastic Processes and Systems2010Inngår i: Mathematical and Statistical Models  and Methods in Reliability :  Applications to Medicine, Finance,  and Quality Control / [ed] V. Rykov, N. Balakrishnan, M. Nikulin, Boston: Birkhäuser , 2010, s. 19-37Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    This paper is a survey of results presented in the recent book: Gyllenberg, M., Silvestrov, D., Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems. De Gruyter Expositions in Mathematics, 44, Walter de Gruyter, Berlin, 2008. This book is devoted to studies of quasi-stationary phenomena for nonlinearly perturbed stochastic processes and systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on 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.

  • 46.
    Silvestrov, Dmitrii
    Mälardalens högskola, Institutionen för matematik och fysik.
    Quasi-stationary phenomena in nonlinearly perturbed stochastc systems2007Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    New methods of asymptotic analysis for nonlinearly perturbed stochstic processes and systems are presented.

  • 47.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Training of Specialists on Educational Measurements in Ukraine.  Part I.2012Collection/Antologi (Fagfellevurdert)
  • 48.
    Silvestrov, Dmitrii
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Borisenko, OlexandrKiev University, Ukraine.
    Proceedings of the International Summer School Insurance and Finance:  Science, Practice       and Education2007Konferanseproceedings (Fagfellevurdert)
  • 49.
    Silvestrov, Dmitrii
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Borisenko, OlexandrKiev University, Ukraine.
    Proceedings of the International Summer School Insurance and Finance: Science, Practice and Education2008Konferanseproceedings (Fagfellevurdert)
  • 50.
    Silvestrov, Dmitrii
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Mälardalen University, School of Education, Culture and Communication.
    Dahlquist, ErikMälardalen University, School of Sustainable Development of Society and Technology .Malyarenko, AnatoliyMälardalen University, School of Education, Culture and Communication.Borisenko, OleksandrKyiv National Taras Shevchenko University, Department of Probability Theory and Mathematical Statistics.
    Proceedings of the International School "Finance, Insurance and Energy Markets - Sustainable Development": A special issue of the Journal of Numerical and Applied Mathematics, 1(96)2008Konferanseproceedings (Annet vitenskapelig)
    Abstract [en]

    The proceedings contains 17 papers based on invited lectures and communications presented at the International School "Finance, Insurance and Energy Markets - Sustainable Development" held in Västerås (Sweden) on 5-9 May, 2008. The paper presented in the proceedings cover the following topics: stochastic modelling of markets, price, trade and risk processes; derivatives, credit ratings and other financial and insurance instruments; simulation, optimisation, and control of energy systems.

123 1 - 50 of 122
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