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  • 1.
    Ekheden, Erland
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Coupling and Explicit Rate of Convergence in Cramer-Lundberg Approximation for Reinsurance Risk Processes2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 19-20, p. 3524-3539Article in journal (Refereed)
    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.

  • 2. Lundgren, Robin
    et al.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Convergence of option rewards for multivariate price processes2009Report (Other academic)
    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.

  • 3.
    Silvestrov, Dimitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Silvestrov, Sergei
    Nonlinearly Perturbed Semi-Markov Processes2017Book (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. 

  • 4.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    A journey in the word of stochastic processes2018In: Stochastic processes and applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer, 2018, p. 7-21Chapter in book (Refereed)
    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.

  • 5.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    A Journey in the World of Stochastic Processes2017Report (Other academic)
    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.

  • 6.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    American-Type Options: Stochastic Approximation Methods, Volume 12014 (ed. 1st)Book (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. 

  • 7.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Improved Asymptotics for Ruin Probabilities2014In: Modern Problems in Insurance Mathematics / [ed] Dimitrii Silvestrov, Anders Martin-Löf, Springer, 2014, p. 37-68Chapter in book (Refereed)
    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.

  • 8.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Individual ergodic theorem for perturbed alternating regenerative processes2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer , 2018, p. 23-89Chapter in book (Refereed)
    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.

  • 9.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Necessary and sufficient conditions for convergence of first-rare-event times for perturbed semi-Markov processes2016Report (Other academic)
    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.

  • 10.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes2016In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 95, p. 119-137Article in journal (Refereed)
    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.

  • 11.
    Silvestrov, Dmitrii
    Stockholm University, Faculty of Science, Department of Mathematics.
    Nonlinearly Perturbed Stochastic Processes and Systems2010In: 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, p. 19-37Chapter in book (Other academic)
    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.

  • 12.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. 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)2008Conference proceedings (editor) (Other academic)
    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.

  • 13.
    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.

     

  • 14.
    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. 

  • 15.
    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.

  • 16.
    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. 

  • 17.
    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.

     

  • 18.
    Silvestrov, Dmitrii
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Manca, Raimondo
    Recurrent Algorithms for Mixed Power: Exponential Moments of Hitting Times for Semi-Markov Processes2017In: Book of Abstracts / [ed] Christos H. Skiadas, 2017, p. 172-172Conference 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.

  • 19.
    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.

  • 20.
    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

  • 21.
    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.

  • 22.
    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. 

  • 23.
    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).

  • 24.
    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.

  • 25.
    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.

  • 26.
    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. 

  • 27.
    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.

  • 28.
    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.

  • 29.
    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.

  • 30.
    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.

  • 31.
    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. 12017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713Article 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.

  • 32.
    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. 22017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713Article 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. 

  • 33.
    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: Institute of Electrical and Electronics Engineers (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.

  • 34.
    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.

  • 35.
    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.

1 - 35 of 35
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