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A Journey in the World of Stochastic Processes
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-2626-5598
2017 (English)Report (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

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2017. , 19 p.
Series
Research report / Mathematical Statistics, ISSN 1650-0377 ; 2017:17
Keyword [en]
Stochastic process, Randomly stopped stochastic process, Perturbed stochastic process, Random walk, Markov chain, Levy process, Markov process, Diffusion process, Renewal process, Generalised exceeding process, Regenerative process, Semi-Markov process, Stochastic process with semi-Markov modulation, Price process, Modulated log-price process, Risk process, Weak convergence limit theorem, Necessary and sufficient condition, U-topology, Skorokhod J-topology, Functional limit theorem, Ergodic theorem, Perturbed renewal equation, Renewal theorem, Coupling, Quasi-stationary distribution, Stochastic approximation, Nonlinear perturbation, Singular perturbation, Asymptotic expansion, Queuing system, Reliability model, Stochastic network, Bio-stochastic system, Ruin probability, American-type option
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-149175OAI: oai:DiVA.org:su-149175DiVA: diva2:1158508
Available from: 2017-11-20 Created: 2017-11-20 Last updated: 2017-11-21Bibliographically approved

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