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3. Modifications of Hitting Times

  • 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 chapter delves into the analysis of extended Markov generalized hitting times, focusing on the conditions for finiteness and upper bounds of their power and exponential moments. It introduces integral equations and serial representations for the expectations of these functionals, providing a rigorous mathematical framework. The text also explores the application of these concepts to semi-Markov processes, particularly those with distributional atoms and artificial regeneration. Additionally, it discusses the implications for multi-alternating regenerative processes modulated by semi-Markov processes. The chapter concludes with a summary of the key findings and their significance in the field of stochastic processes.
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previous chapter Summary of Ergodic Theorems for Regenerative Processes
next chapter Birth-Death-Type Processes
Title
Modifications of Hitting Times
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_3

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