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  • 101.
    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. 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 sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces.

  • 102.
    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. II2016Report (Other academic)
  • 103.
    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 perturbed semi-Markov processes2016Report (Other academic)
  • 104.
    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 Perturbed Semi-Markov Processes2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Chapter in book (Refereed)
    Abstract [en]

    New algorithms for computing asymptotic expansions for 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 processes with asymptotically coupled and uncoupled finite phase spaces.

  • 105.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Mälardalen University, Sweden.
    Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov, Milica Rančić, Cham: Springer, 2016, p. 151-222Chapter in book (Refereed)
    Abstract [en]

    New algorithms for computing of asymptotic expansions for 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 processes with asymptotically coupled and uncoupled finite phase spaces.

  • 106.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes2016In: Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management (SMRLO 2016): Proceedings / [ed] Ilia Frenkel, Anatoly Lisnianski, New York, USA: IEEE, 2016, p. 41-46Conference paper (Refereed)
    Abstract [en]

    New algorithms for computing asymptotic expansions for power moments of hitting times and 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.

  • 107.
    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.
    Nonlinearly Perturbed Semi-Markov Processes2017 (ed. 1)Book (Refereed)
    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. 

  • 108.
    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.
    Abola, Benard
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Coupling and Ergodic Theorems for Markov Chains with Damping Component2019In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 101, p. 212-231Article in journal (Refereed)
    Abstract [en]

    Perturbed Markov chains are popular models for description of information networks. Insuch models, the transition matrix P0 of an information Markov chain is usually approximated bymatrix Pε = (1-ε)P0+εD, where D is a so-called damping stochastic matrix with identical rowsand all positive elements, while ε [0; 1] is a damping (perturbation) parameter. Using procedure ofarticial regeneration for the perturbed Markov chain ηε,n with the matrix of transition probabilities Pε , and coupling methods, we get ergodic theorems, in the form of asymptotic relations for Pε,ij (n) =Pi {ηε,n =j}, as n  and ε0, and explicit upper bounds for the rates of convergence in such theorems. In particular, the most dicult case of the model with singular perturbations, wherethe phase space of the unperturbed Markov chain η0,n split in several closed classes of communicativestates and possibly a class of transient states, is investigated.

  • 109.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Abola, Benard
    Biganda, Pitos S.
    Engström, Christopher
    Mango, John M.
    Kakuba, Godvingod
    Coupling and Ergodic Theorems for Markov Chains with Damping Component2019In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 101, p. 212-231Article in journal (Refereed)
    Abstract [en]

    Coupling method is used for geting ergodic theorems for perturbed Markov chains with damping component and rates of convergence in such theorems.

  • 110.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Umeå University, Sweden.
    Silvestrova, Evelina
    Elsevier's Dictionary of Statistical Terminology: English-Russian, Russian-English1995Book (Refereed)
    Abstract [en]

    This is English-Russian, Russian-English disctionary of statistical terminology, which contains approximatelly 14,000 terminalogical units and includes bilingual name indices representing about 1,000 names appearing in the dictionary.

  • 111.
    Silvestrov, Dmitrii
    et al.
    Department of Mathematics Stockholm University,.
    Silvestrova, Evelina
    Mälardalen University, School of Education, Culture and Communication.
    Manva, Raimondo
    Università di Roma.
    Stochastically ordered models for credit rating dynamics2008In: J. Numer. Appl. Math., ISSN 0868-6912, Vol. 1, p. 206-215Article in journal (Refereed)
  • 112.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    A pricing process with stochastic volatility controlled by a semi-Markov process2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 591-608Article in journal (Refereed)
    Abstract [sv]

    This paper is devoted to the investigation of the geometrical Brownian motion as a price process where the drift and volatility are controlled by a semi-Markov process. Conditions of risk-neutral measure are given as well as a formula for the risk-neutral price for European options. The discrete version, the binomial model controlled by a semi-Markov chain, is examined and limit theorems describing the transition from discrete time binomial to continuous time model are given. A system of partial differential equations for distribution functions of average volatility is given. Related Monte Carlo algorithms are described.

  • 113.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef
    Catholic University of Leuven, Belgium.
    Masol, Viktoriya
    Mälardalen University, Department of Mathematics and Physics.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Innovation methods, algorithms, and software for analysis of reinsurance contracts2006In: Theory of Stochastic Processes, ISSN 0095-7380, Theory of Stochastic Processes, ISSN 0095-7380, Vol. 12(28), no 3-4, p. 203-238Article in journal (Refereed)
    Abstract [en]

     A Monte Carlo based approach to evaluate and/or compare the riskiness of reinsurance treaties for both the ceding and the reinsurance companies is introduced. An experimental program system Reinsurance Analyser based on the indicated approach is presented. The program allows ana-lyzing applications of a large set of reinsurance contracts under a variety of claim flow models. The effect of applications is compared by risk mea-sures, provided that the parameters of the contracts are balanced by an average reinsurer's load quantity.

  • 114.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef
    Catholic University of Leuven, Belgium.
    Masol, Viktoriya
    Mälardalen University, Department of Mathematics and Physics.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Reinsurance Analyser2005Report (Other academic)
    Abstract [en]

    A Monte Carlo based program system for analysis of reinsurance contracts is described. new method for compariso of reinsurance contracts are presented. Results of computer experimental studies are presented and commented.

  • 115.
    Silvestrov, D.S.
    Mälardalen University, Department of Mathematics and Physics.
    Limit theorems for randomly stopped stochastic processes2006In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Journal of Mathematical Sciences, ISSN 1072-3374, Vol. 138, no 1, p. 5467-5471Article in journal (Refereed)
    Abstract [en]

    General conditions of weak and J-convergence for superposition of stochastic processes are formulated

  • 116.
    Silvestrov, D:S.
    Mälardalen University, Department of Mathematics and Physics.
    Limit Theorems for Randomly Stopped Stochstic Processes2004Book (Refereed)
    Abstract [en]

    The book presents general limit theorems about weak convergence of randomly stopped stochastic processes and compositions of stochastic processes as well as functional limit theorems for compositions of stochastic processes. Applications to random sums, extremes with random sample size, sum- and max-processes with renewal type stopping, accumulation processes, and shock processes are given.

  • 117.
    Stenberg, F.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Manca, R.
    Silvestrov, D.
    Mälardalen University, Department of Mathematics and Physics.
    Discrete Time Backward Semi-Markov Reward Processes and an Aplication to Disability Insurance Problems2005Report (Other academic)
    Abstract [en]

    Semi-Markov reward backward processes are studied. Algorithms for evaluation of higher moments for rewards are described. Application to analysis of semi-Markov reward models of disability insurance contracts are considered.

  • 118.
    Stenberg, Fredrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Manca, R.
    University of Rome "La Sapienza", Italy.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward2007In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 9, no 4, p. 497-519Article in journal (Refereed)
    Abstract [en]

    In this paper semi-Markov reward models are presented. Higher moments of the reward process are presented for the first time and applied to in time non-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described.

  • 119.
    Stenberg, Fredrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Manca, Raimondo
    Silvestrov, Dmitrii
    An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes with an application to disability insurance2007In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 9, no 4, p. 497-519Article in journal (Refereed)
    Abstract [en]

    In this paper semi-Markov reward models are presented. Higher moments of the reward process is presented for the first time applied to in timenon-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described.

  • 120.
    Stenberg, Fredrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Manca, Raimondo
    Silvestrov, Dmitrii
    Discrete Time Backward Semi-Markov Reward Processes and an Application to Disability Insurance ProblemsManuscript (Other academic)
  • 121.
    Stenberg, Fredrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Manca, Raimondo
    Rome University.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    SEMI-MARKOV REWARD MODELS FOR DISABILITY INSURANCE2006In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 239-254Article in journal (Refereed)
    Abstract [en]

    A semi-Markov model for disability insurance is described. Statisticalevidences of relevance semi-Markov setting are given. High order semiMarkov backward reward models are invented. Applications of these models to profit-risk analysis of disability insurance contracts are considered.

  • 122.
    Stenberg, Fredrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Manca, R.
    University of Rome, Italy.
    Semi-Markov reward models for disability insurance2006In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 239-254Article in journal (Refereed)
    Abstract [en]

    A semi-Markov model for disability insurance is described. Statistical evidences of relevance semi-Markov setting are given. High order semi-Markov backward reward models are invented. Applications of these models to profit-risk analysis of disability insurance contracts are considered.

123 101 - 122 of 122
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