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  • 51.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Upper bounds for exponential moments of hitting times for semi-Markov processes2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 533-544Article in journal (Refereed)
    Abstract [en]

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

  • 52.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, M.O.
    Mälardalen University, Department of Mathematics and Physics.
    Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. I2006In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 151-186Article in journal (Refereed)
    Abstract [en]

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

  • 53.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Drozdenko, M.O.
    Mälardalen University, Department of Mathematics and Physics.
    Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. II2006In: Theory of Stochstic Processes, ISSN 0321-3900, Vol. 12(28), no 3-4, p. 187-202Article in journal (Refereed)
    Abstract [en]

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

  • 54.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jönsson, Henrik
    Mälardalen University, Department of Mathematics and Physics.
    Kukush, Alexander G.
    Kiev University, Ukraine.
    Optimal stopping strategies for American type options2004Conference paper (Other academic)
  • 55.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Malyarenko, Anatoliy
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrova, Evelina
    Mälardalen University, Department of Mathematics and Physics.
    Stochastic modelling of insurance business with dynamical control of investments2004In: 3rd Conference in Actuarial Science & Finance in Samos, Karlovassi, September 2-5 2004, 2004, p. page 54-Conference paper (Other academic)
  • 56.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Mishura, Yu.S.
    Mälardalen University, Department of Mathematics and Physics.
    Limit theorems for stochastic Riemann-Stieltjes integrals2004In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 10(26), p. 122-140Article in journal (Refereed)
  • 57.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Silvestrova, Evelina
    Mälardalen University, Department of Mathematics and Physics.
    Master programmes in analytical finance at Mälardalen University2004Conference paper (Other academic)
  • 58.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    Pricing process with stochastic volatility controlled by a semi-Markov process in option pricing2004Conference paper (Other academic)
  • 59.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef
    Katholieke Universiteit Leuven, Belgium..
    Limit theorems for mixed max-sum processes with renewal stopping2004Conference paper (Other academic)
  • 60.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Teugels, Jozef L.
    Katholieke Universiteit Leuven, Belgium.
    Limit theorems for mixed max-sum processes with renewal stopping2004In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 14, no 4, p. 1838-1868Article in journal (Refereed)
    Abstract [en]

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

  • 61.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Yadrenko, M.I.
    Mälardalen University, Department of Mathematics and Physics.
    Zinchenko, N.M.
    Mälardalen University, Department of Mathematics and Physics.
    Improvement of economic-statistical education in Ukraine and TEMPUS Networking project 22012-2001 (In: Proceedings of the Eighth International2004In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 10, no 26, p. 162-171Article in journal (Refereed)
  • 62.
    Silvestrov, Dmitrii S.
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Yadrenko, Mikhailo
    Mälardalen University, Department of Mathematics and Physics.
    Zinchenko, Nadiia
    Mälardalen University, Department of Mathematics and Physics.
    Improvement of economic-statistical education in Ukraine and Tempus Networking project 22012-20012004Conference paper (Other academic)
  • 63.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Sergienko, V.Kovalchuk, Yuriy
    Proceedings of the International Summer School “Educational Measurements: Teaching, Research, and Practice”2010Conference proceedings (editor) (Refereed)
  • 64.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic expansions for power-exponential moments of hitting times for nonlinearly perturbed semi-Markov processes2017In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 171-187Article in journal (Refereed)
    Abstract [en]

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

  • 65.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic expansions for stationary and quasi-stationary distributions of perturbed semi-Markov processes2017In: AIP Conference Proceedings / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020147-1-020147-9, article id 020147Conference paper (Refereed)
    Abstract [en]

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

  • 66.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 12019In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 945-964Article in journal (Refereed)
    Abstract [en]

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

  • 67.
    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.

  • 68.
    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)
  • 69.
    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)
  • 70.
    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.

  • 71.
    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. 

  • 72.
    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)
  • 73.
    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.

  • 74.
    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.

  • 75.
    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.

  • 76.
    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

  • 77.
    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.

  • 78.
    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.

  • 79.
    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.

  • 80.
    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.

  • 81.
    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)
  • 82.
    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.

  • 83.
    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.

12 51 - 83 of 83
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