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Coupling and Ergodic theorems for se...

Silʹvestrov, D. S.

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Coupling and Ergodic theorems for semi-Markov-type processes.. II,. Semi-Markov processes and multi-alternating regenerative processes with semi-markov modulation

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Coupling and Ergodic theorems for semi-Markov-type processes./ by Dmitrii Silvestrov.
其他題名:	Semi-Markov processes and multi-alternating regenerative processes with semi-markov modulation
作者:	Silʹvestrov, D. S.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xix, 560 p. :ill., digital ;24 cm.
內容註:	Preface -- Introduction -- Summary of Ergodic Theorems for Regenerative Processes -- Modifications of Hitting Times -- Birth-Death-Type Processes -- Semi-Markov Processes with Discrete State Spaces and Embedded Regenerative Processes -- Ergodic Theorems for Queuing Systems -- Semi-Markov Processes with General State Spaces with Atoms -- Semi-Markov Processes with General State Spaces and Distributional Atoms -- Semi-Markov Processes with General State Spaces and One-Step Artificial Regeneration -- Semi-Markov Processes with General State Spaces and Multi-Step Artificial Regeneration -- Multi-Alternating Regenerative Processes with Semi-Markov Modulation -- Multi-Alternating Regenerative Processes Modulating by Uniformly Recurrent Semi-Markov Processes -- Appendix A. Methodological and Bibliographical Notes -- References -- Index.
Contained By:	Springer Nature eBook
標題:	Markov processes. -
電子資源:	https://doi.org/10.1007/978-3-031-89315-5
ISBN:	9783031893155

Coupling and Ergodic theorems for semi-Markov-type processes.. II,. Semi-Markov processes and multi-alternating regenerative processes with semi-markov modulation
Silʹvestrov, D. S.

Coupling and Ergodic theorems for semi-Markov-type processes.II,Semi-Markov processes and multi-alternating regenerative processes with semi-markov modulation[electronic resource] /Semi-Markov processes and multi-alternating regenerative processes with semi-markov modulationby Dmitrii Silvestrov. - Cham :Springer Nature Switzerland :2025. - xix, 560 p. :ill., digital ;24 cm.

Preface -- Introduction -- Summary of Ergodic Theorems for Regenerative Processes -- Modifications of Hitting Times -- Birth-Death-Type Processes -- Semi-Markov Processes with Discrete State Spaces and Embedded Regenerative Processes -- Ergodic Theorems for Queuing Systems -- Semi-Markov Processes with General State Spaces with Atoms -- Semi-Markov Processes with General State Spaces and Distributional Atoms -- Semi-Markov Processes with General State Spaces and One-Step Artificial Regeneration -- Semi-Markov Processes with General State Spaces and Multi-Step Artificial Regeneration -- Multi-Alternating Regenerative Processes with Semi-Markov Modulation -- Multi-Alternating Regenerative Processes Modulating by Uniformly Recurrent Semi-Markov Processes -- Appendix A. Methodological and Bibliographical Notes -- References -- Index.

Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This book is the second volume of a two-volume monograph dedicated to ergodic theorems. While the first 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 and delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates for such processes. The book offers a powerful and constructive probabilistic framework by employing coupling ergodic theorems presented in the first volume in conjunction with the method of artificial regeneration and test functions. Theoretical findings are illustrated with applications to semi-Markov Monte Carlo algorithms and perturbed queuing systems featuring explicit convergence rate bounds. Many results presented in the book are groundbreaking, appearing in publication for the first time. 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: 9783031893155

Standard No.: 10.1007/978-3-031-89315-5doiSubjects--Topical Terms:

532104
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

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520 $a Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This book is the second volume of a two-volume monograph dedicated to ergodic theorems. While the first 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 and delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates for such processes. The book offers a powerful and constructive probabilistic framework by employing coupling ergodic theorems presented in the first volume in conjunction with the method of artificial regeneration and test functions. Theoretical findings are illustrated with applications to semi-Markov Monte Carlo algorithms and perturbed queuing systems featuring explicit convergence rate bounds. Many results presented in the book are groundbreaking, appearing in publication for the first time. 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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