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11. Multi-alternating Regenerative Processes with Semi-Markov Modulation

  • 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 intricate world of multi-alternating regenerative processes with semi-Markov modulation, presenting ergodic theorems with explicit power and exponential upper bounds for convergence rates. The text introduces these processes, which generalize both regenerative and semi-Markov processes, and provides renewal-type equations for their distributions. It explores thinned multi-alternating regenerative processes and their properties, including ergodicity conditions and relations connecting stationary distributions. The chapter also presents ergodic theorems for processes with atoms and those admitting artificial regeneration, offering stability and ergodic relations with explicit bounds. The concluding remarks highlight the versatility of these processes in modeling various applied stochastic systems, such as queuing, reliability, and financial processes. The chapter concludes with a discussion on the most general ergodic theorems for semi-Markov-type processes, emphasizing their applicability and the reduction to simpler cases under specific conditions.
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previous chapter Semi-Markov Processes with General State Spaces and Multi-step Artificial Regeneration
next chapter Multi-alternating Regenerative Processes Modulated by Uniformly Recurrent Semi-Markov Processes
Title
Multi-alternating Regenerative Processes with Semi-Markov Modulation
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_11

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