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Coupling and Ergodic theorems for semi-Markov-type processes.I,Markov chains, renewal, and regenerative processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Coupling and Ergodic theorems for semi-Markov-type processes.by Dmitrii Silvestrov.
remainder title:	Markov chains, renewal, and regenerative processes
Author:	Silʹvestrov, D. S.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xix, 611 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Markov processes.
Online resource:	https://doi.org/10.1007/978-3-031-89311-7
ISBN:	9783031893117$q(electronic bk.)

Coupling and Ergodic theorems for semi-Markov-type processes.I,Markov chains, renewal, and regenerative processes
Silʹvestrov, D. S.

Coupling and Ergodic theorems for semi-Markov-type processes.I,Markov chains, renewal, and regenerative processes[electronic resource] /Markov chains, renewal, and regenerative processesby Dmitrii Silvestrov. - Cham :Springer Nature Switzerland :2025. - xix, 611 p. :ill., digital ;24 cm.

Preface -- Introduction -- Coupling for Random Variables -- Coupling and Ergodic Theorems for Finite Markov Chains -- Coupling and Ergodic Theorems for General Markov Chains -- Hitting Times and Method of Test Functions -- Approaching of Renewal Schemes -- Synchronizing of Shifted Renewal Schemes -- Coupling for Renewal Schemes -- Coupling and Ergodic Theorems for Regenerative Processes -- Uniform Ergodic Theorems for Regenerative Processes -- Generalized Ergodic Theorems for Regenerative Processes -- Coupling and the Renewal Theorem -- Appendix A. Basic Ergodic Theorems for Regenerative Processes -- Appendix B. Methodological and Bibliographical Notes -- References -- Index.

Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds. Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.

ISBN: 9783031893117$q(electronic bk.)

Standard No.: 10.1007/978-3-031-89311-7doiSubjects--Topical Terms:

181910
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

Coupling and Ergodic theorems for semi-Markov-type processes.I,Markov chains, renewal, and regenerative processes
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505 0 $a Preface -- Introduction -- Coupling for Random Variables -- Coupling and Ergodic Theorems for Finite Markov Chains -- Coupling and Ergodic Theorems for General Markov Chains -- Hitting Times and Method of Test Functions -- Approaching of Renewal Schemes -- Synchronizing of Shifted Renewal Schemes -- Coupling for Renewal Schemes -- Coupling and Ergodic Theorems for Regenerative Processes -- Uniform Ergodic Theorems for Regenerative Processes -- Generalized Ergodic Theorems for Regenerative Processes -- Coupling and the Renewal Theorem -- Appendix A. Basic Ergodic Theorems for Regenerative Processes -- Appendix B. Methodological and Bibliographical Notes -- References -- Index.
520 $a Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds. Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.
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