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7. Semi-Markov Processes with General State Spaces with Atoms

  • 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 presents a comprehensive analysis of semi-Markov processes with general state spaces and atoms, focusing on ergodic theorems and explicit upper bounds for convergence rates. The text introduces the concept of semi-Markov processes with atoms and defines their accompanying Markov processes. It provides recurrence conditions for subsets of the state space and evaluates weighting parameters for absolutely continuous components of distribution functions of regeneration times. The chapter also presents necessary and sufficient conditions for the finiteness and upper bounds of power and exponential moments of regeneration times and transition periods. Additionally, it explores stationary distributions for semi-Markov processes with atoms and their accompanying Markov processes. The text concludes with ergodic theorems that provide explicit upper bounds for convergence rates, making it a valuable resource for professionals in the field of stochastic processes and Markov chains.
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previous chapter Ergodic Theorems for Queuing Systems
next chapter Semi-Markov Processes with General State Spaces and Distributional Atoms
Title
Semi-Markov Processes with General State Spaces with Atoms
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_7
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