Nonlinearly perturbed semi-Markov processes

✍ Scribed by Silʹvestrov, Dmitriĭ Sergeevich; Silvestrov, Sergei D

Publisher: Springer
Year: 2017
Tongue: English
Leaves: 151
Series: SpringerBriefs in Probability and Mathematical Statistics
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xiv
Introduction (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 1-15
Laurent Asymptotic Expansions (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 17-35
Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 37-66
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 67-79
Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 81-106
Examples and Survey of Applied Perturbed Stochastic Models (Dmitrii Silvestrov, Sergei Silvestrov)....Pages 107-121
Back Matter ....Pages 123-143

✦ Subjects

Markov processes;MATHEMATICS / Applied;MATHEMATICS / Probability & Statistics / General

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