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1. Introduction

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Author
Dmitrii Silvestrov
Published in
Coupling and Ergodic Theorems for Semi-Markov-Type Processes II
Publisher
Springer Nature Switzerland

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Abstract

The book is the second volume of a two-volume monograph, focusing on ergodic theorems with explicit upper bounds for convergence rates for semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. It introduces the main problems, methods, and algorithms, using simple examples and figures to illustrate the logic and ideas underlying the method of test functions and the method of artificial regeneration. The book covers various classes of stochastic processes, including regenerative and semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. It presents ergodic theorems for these processes, using the method of test functions to obtain upper bounds for power and exponential moments of hitting times. The book also discusses applications of these theorems to queuing systems, semi-Markov Monte Carlo algorithms, and the semi-Markov renewal theorem. Each chapter includes a preamble, main theorems, lemmas, and a short conclusion with comments. The book concludes with a bibliography, terminological index, and lists of common symbols and abbreviations.
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next chapter Summary of Ergodic Theorems for Regenerative Processes
Title
Introduction
Author
Dmitrii Silvestrov
Copyright Year
2025
Book
Coupling and Ergodic Theorems for Semi-Markov-Type Processes II

Print ISBN: 978-3-031-89314-8

Electronic ISBN: 978-3-031-89315-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-89315-5_1

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