Perturbed semi-Markov type processes. I, Limit theorems for rare-event times and processes / Dmitrii Silvestrov.
Silʹvestrov, D. S. (Dmitriĭ Sergeevich), author.
2022
QA274.7 .S55 2022
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Title Perturbed semi-Markov type processes. I, Limit theorems for rare-event times and processes / Dmitrii Silvestrov.
Author Silʹvestrov, D. S. (Dmitriĭ Sergeevich), author.
ISBN 9783030924034 (electronic bk.)
3030924033 (electronic bk.)
9783030924027
DOI https://doi.org/10.1007/978-3-030-92403-4
Published Cham : Springer, [2022]
Copyright ©2022
Language English
Description 1 online resource (xvii, 401 pages) : illustrations (some color)
Other Standard Identifiers 10.1007/978-3-030-92403-4 doi
Call Number QA274.7 .S55 2022
Dewey Decimal Classification 519.2/33
Summary 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 multi-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. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications. .
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 29, 2022).
Available in Other Form Perturbed semi-Markov type processes. Volume 1, Limit theorems for rare-event times and processes.
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Preface
List of symbols
Introduction
Part I: First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes
Flows of Rare Events for Regularly Perturbed Semi-Markov Processes
Generalizations of Limit Theorems for First-Rare-Event Times
First-Rare-Event Times for Perturbed Risk Processes
First-Rare-Event Times for Perturbed Closed Queuing Systems
First-Rare-Event Times for Perturbed M/M-Type Queuing Systems
Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes
Asymptotically Comparable Functions
Perturbed Semi-Markov Processes and Reduction of Phase Space
Asymptotics of Hitting Times for Perturbed Semi-Markov Processes
Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes
Generalizations and Examples of Limit Theorems for Hitting Times
Limit Theorems for Randomly Stopped Stochastic Processes
Methodological and Bibliographical Notes
References
Index.

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