Algorithms of Phase Space Reduction and Asymptotics of Hitting Times for Perturbed Semi-Markov Processes

2019/07/08 by Dmitrii Silvestrov, Silvestrov, Dmitrii
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #60J10 #60J22 #60J27 #60K15 #65C40 #Advanced Research in Systems and Signal Processing #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Control Systems and Analysis #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60J22 #msc:60J27 #msc:60K15 #msc:65C40

paper · pdf · doi:10.48550/arxiv.1907.03529

142 pages

arxiv created 2019/07/08 · openalex publication_date 2019/07/08 · arxiv updated 2019/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence of expectations for hitting times as well as recurrent formulas for computing the corresponding normalisation functions, Laplace transforms for limiting distributions and limits for expectations.

Citations

• Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes

Related

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• Necessary and Sufficient Conditions for Convergence of First-Rare-Event Times for Perturbed Semi-Markov Processes
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