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  • 1.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Biganda, Pitos Seleka
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John Magero
    Makerere University.
    Kakuba, Godwin
    Makerere University.
    Perturbed Markov chains and information networksManuscript (preprint) (Other academic)
  • 2.
    Abola, Benard
    et al.
    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.
    Silvestrov, Dmitrii
    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.
    Mango, John
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Nonlinearly  Perturbed Markov Chains  and  Information Networks2019In: 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, p. 51-79Conference paper (Refereed)
    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.

  • 3.
    Abola, Benard
    et al.
    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.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John Magero
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks2021In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, Hoboken, NJ: John Wiley & Sons, 2021, p. 23-55Chapter in book (Refereed)
    Abstract [en]

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

  • 4. Biffi, Elena
    et al.
    D'Amico, Guillermo
    Di Biase, G
    Janssen, J
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules II2008In: Journal of Numerical and Applied Mathematics, Vol. 96, p. 59-86Article in journal (Refereed)
  • 5. Biffi, Elena
    et al.
    D'Amigo, Guillermo
    Di Biase, Giuseppe
    Janssen, Jacques
    Manca, Raimondo
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules. I.2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 1, p. 28-58Article in journal (Refereed)
  • 6.
    Drozdenko, M.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, D.
    Mälardalen University, Department of Mathematics and Physics.
    On necessary and sufficient conditions for approximations of ruin probabilities2004Conference paper (Other academic)
    Abstract [en]

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

  • 7.
    Ekheden, Erhard
    et al.
    Stockholm University.
    Silvestrov, Dmitrii
    Stockholm University.
    Coupling and explicit rates of convergence in Cramér-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 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.

  • 8.
    Jönsson, H.
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Kukush, A. G.
    Kyiv University, Kyiv, 01033, Ukraine.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Threshold structure of optimal stopping strategies for american type option. II2006In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 72, p. 47-58Article in journal (Refereed)
    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. © 2006 American Mathematical Society.

  • 9.
    Jönsson, H.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, A.G.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, D.
    Mälardalen University, Department of Mathematics and Physics.
    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), 170-1772004Licentiate thesis, monograph (Other scientific)
    Abstract [en]

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

  • 10.
    Jönsson, Henrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Domains for American Type Options2002In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 8, no 1-2, p. 169-176Article in journal (Other academic)
  • 11.
    Jönsson, Henrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Strategies for American Type Option. I2004In: Theory of Probability and Mathematical Statistics, ISSN 1547-7363, Vol. 71, p. 82-92Article in journal (Refereed)
    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, Henrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Threshold structure of optimal stopping strategies for American type options2004Report (Other academic)
  • 13.
    Jönsson, Henrik
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander
    Silvestrov, Dmitrii
    Threshold Structure of Optimal Stopping Strategies for American Type Options. II2005In: Theory of Probability and Mathematical Statistics, ISSN 1547-7363, Vol. 72, p. 42-53Article in journal (Refereed)
    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.

  • 14.
    Jönsson, Jönsson
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, A.G.
    Kiev University, Ukraine.
    Silvestrov, D.S.
    Mälardalen University, Department of Mathematics and Physics.
    Optimal stopping strategies for American type options2004Conference paper (Other academic)
    Abstract [en]

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

  • 15.
    Kukush, Alexander G.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Optimal pricing of American type options with discrete time2004In: Theory of Stochastic Processes, Vol. 10, no 26, p. 72-96Article in journal (Refereed)
  • 16.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Convergence and Approximation of Option Rewards for Multivariate Price Processes2009Report (Other (popular science, discussion, etc.))
    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.

  • 17.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Optimal stopping and reselling of European options2010In: Mathematical and Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishan, N., Nikulin, M, Boston: Birkhäuser , 2010Chapter in book (Refereed)
    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. 

  • 18.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Kukush, Alexander
    Kiev University.
    Reselling of options and convergence of option rewards2008In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 30, no 3-4Article in journal (Refereed)
    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

  • 19.
    Malyarenko, Anatoliy
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrov, Dmitrii S.
    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: 6th World Congress of Bernoulli Society for Mathematical Statistics and Probability, Barcelona, July 26--31 2004, 2004, p. page 181-Conference paper (Other academic)
  • 20.
    Manca, R.
    et al.
    Universit´a di Roma La Sapienza, Italy.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    Homogeneous backward semi-Markov reward models for insurance contracts2005In: Proceedings of ASMDA 2005 Conference: Brest, 2005, 2005, p. 959-967Conference paper (Other academic)
    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.

  • 21.
    Ni, Ying
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Dmitrii
    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.
    Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbations2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, no 1, p. 173-197Article in journal (Refereed)
    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.

  • 22.
    Silvestrov, D.
    Mälardalen University, Department of Mathematics and Physics.
    About my teacher2005In: In World of Mathematics, Vol. 11, no 1, p. 33-37Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

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

  • 23.
    Silvestrov, D.
    Mälardalen University, Department of Mathematics and Physics.
    Quasi-stationary phenomena in nonlinearly perturbed stochstic systems2006Conference paper (Other (popular science, discussion, etc.))
    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

  • 24.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Borisenko, O.
    Proceedings of the International Summer School “Insurance and Finance: Science, Practice and Education”: Foros, 20062006Conference proceedings (editor) (Refereed)
  • 25.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Borisenko, O.Kiev University, Ukraine.
    Proceedings of the International Summer School “Insurance and Finance: Science, Practice and Education": Foros, 20072007Conference proceedings (editor) (Refereed)
  • 26.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, M.
    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 Theory2005Report (Other academic)
    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.

  • 27.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jonsson, H.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, F.
    Mälardalen University, Department of Mathematics and Physics.
    Convergence of option rewards for Markov type price processes2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 189-200Article in journal (Other (popular science, discussion, etc.))
    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

  • 28.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jönsson, H.
    Mälardalen University, Department of Mathematics and Physics.
    Stanberg, F.
    Mälardalen University, Department of Mathematics and Physics.
    Convergence of Option Rewards for Markov Type Price Processes Controlled by Stochastic Indicies. 12006Report (Other academic)
    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

  • 29.
    Silvestrov, D.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jef
    Catholic University of Leuven, Belgium.
    Masol, Viktoriya
    Kyiv National Taras Shevchenko University, Ukraine.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Reinsurance analyser2006In: International Conference Modern Stochastics: Theory and Applications: Dedicated to the 60th anniversary of the Department of ProbabilityTheory and Mathematical Statistics and to the memory ofProfessor M.Y. Yadrenko (1932-2004)Conference Materials, 2006, p. 245-Conference paper (Other academic)
    Abstract [en]

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

  • 30.
    Silvestrov, Dmitrii
    Stockholm University, Sweden.
    A journey in the word of stochastic processes2018In: Stochastic processes and applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Silvestrov, S., Rancic, Malyarenko, A., 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.

  • 31.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    American-Type Options, Stochastic Approximation Methods, Volume 22015Book (Refereed)
  • 32.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    American-Type Options:  Stochastic Approximation Methods. Volume I2014Book (Refereed)
  • 33.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Asymptotic expansions for distributions of the surplus prior and at the time of ruin2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 183-188Article in journal (Refereed)
    Abstract [en]

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

  • 34.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Asymptotic expansions for quasi-stationary distributions of nonlinearly perturbed semi-Markov processes2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 1-2, p. 267-271Article in journal (Refereed)
    Abstract [en]

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

  • 35.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Convergence in distribution for randomly stopped random fields2021In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 105, p. 137-149Article in journal (Refereed)
    Abstract [en]

    Let X and Y be two complete, separable, metric spaces, xi(epsilon)(x), x is an element of X and nu(epsilon) be, for every epsilon is an element of[0, 1], respectively, a random field taking values in space Y and a random variable taking values in space X. We present general conditions for convergence in distribution for random variables xi(epsilon)(nu(epsilon)) that is the conditions insuring holding of relation, xi(epsilon)(nu(epsilon)) d ->xi(0)(nu(0)) as epsilon -> 0.

  • 36.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Convergence in Skorokhod J-topology for compositions of stochastic processes2008In: Theory Stoch. Process., ISSN 0321-3900, Vol. 14, no 1, p. 126-143Article in journal (Refereed)
    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.

  • 37.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Improved Asymptotics for Ruin Probabilities2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, p. 37-68Chapter in book (Refereed)
    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.

  • 38.
    Silvestrov, Dmitrii
    Stockholm University, Sweden.
    Individual ergodic theorem for perturbed alternating regenerative processes2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Silvestrov, S., Rancic, M., Malyarenko, A., 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.

  • 39.
    Silvestrov, Dmitrii
    Stockholm University, Sweden.
    Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes2016In: Theory of Probability and Mathematical Statistics, 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.

  • 40.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Nonlinearly perturbed stochastic processes2008In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 14, no 3-4, p. 129-164Article in journal (Refereed)
    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.

  • 41.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Nonlinearly perturbed stochastic processes and systems2011In: Mathematical and  Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishnan, N., Nikulin, M., Boston: Birkhäuser Verlag, 2011, p. 19-34Chapter in book (Refereed)
    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. 

  • 42.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes2022 (ed. 1)Book (Refereed)
    Abstract [en]

    This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes; new asymptotic recurrent algorithms of phase space reduction  and effective conditions of weak convergence for distributions of hitting times and convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes.

  • 43.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Perturbed Semi-Markov Type Processes II: Ergodic Theorems for Multi-Alternating Regenerative Processes2022 (ed. 1)Book (Refereed)
    Abstract [en]

    This book is the second volume of two volumes monograph devoted to the study of limit  and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes,  and alternating regenerative processes with semi-Markov modulation. The second volume presents new super-long, long and short time ergodic theorems for perturbed alternating regenerative processes and multi-alternating regenerative processes  modulating by regularly and singularly perturbed finite semi-Markov processes. 

  • 44.
    Silvestrov, Dmitrii
    Mälardalen University, Department of Mathematics and Physics.
    Quasi-stationary phenomena in nonlinearly perturbed stochastc systems2007Conference paper (Other academic)
    Abstract [en]

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

  • 45.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Training of Specialists on Educational Measurements in Ukraine.  Part I.2012Collection (editor) (Refereed)
  • 46.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Borisenko, OlexandrKiev University, Ukraine.
    Proceedings of the International Summer School Insurance and Finance:  Science, Practice       and Education2007Conference proceedings (editor) (Refereed)
  • 47.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Borisenko, OlexandrKiev University, Ukraine.
    Proceedings of the International Summer School Insurance and Finance: Science, Practice and Education2008Conference proceedings (editor) (Refereed)
  • 48.
    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)
  • 49.
    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.

  • 50.
    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.

12 1 - 50 of 100
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