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2. Summary of Ergodic Theorems for Regenerative Processes

  • 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

This chapter delves into the summary of coupling ergodic theorems with explicit upper bounds for convergence rates for regenerative processes. It begins by revisiting the constructive definitions of regenerative processes and their thinned versions, emphasizing the weighting absolute continuity condition, which is pivotal for deriving ergodic theorems. The chapter then presents ergodic theorems with explicit power and exponential upper bounds for convergence rates, providing a thorough exploration of the conditions and constants involved. Key topics include the definitions and properties of regenerative processes, the conditions for ergodicity, and the explicit bounds for convergence rates. The chapter concludes with a discussion on the application of these theorems to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation, highlighting the practical implications of these theoretical results. Readers will gain a deeper understanding of the stability and ergodicity of regenerative processes, as well as the methods used to derive explicit bounds for convergence rates.
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previous chapter Introduction
next chapter Modifications of Hitting Times
Title
Summary of Ergodic Theorems for Regenerative Processes
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_2

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