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4. Birth-Death-Type 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 intricate world of semi-Markov birth-death-type processes, focusing on ergodic theorems and explicit upper bounds for convergence rates. The text begins by presenting ergodic theorems that provide stability and ergodic relations for these processes. It then explores various upper bounds for power and exponential moments of hitting times, using methods such as test functions and recurrent relations. The chapter includes numerous lemmas and theorems that offer detailed insights into the behavior of these processes. The text concludes with a discussion on the applications of these results in bio-stochastic models and queuing systems, highlighting the importance of ergodic theorems in these fields. Readers will gain a deeper understanding of the theoretical underpinnings and practical applications of semi-Markov birth-death-type processes, making this chapter a valuable resource for professionals in the field.
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previous chapter Modifications of Hitting Times
next chapter Semi-Markov Processes with Discrete State Spaces and Embedded Regenerative Processes
Title
Birth-Death-Type 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_4
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