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3. Recurrence

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Authors
Hai-Dang Nguyen
George Yin
Chao Zhu
Published in
Hybrid Switching Diffusions
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the recurrence of switching diffusion processes, focusing on their asymptotic behavior and stability. It introduces key concepts such as weak-sense stability, Lyapunov functions, and the definitions of recurrence, positive recurrence, and null recurrence. The text provides a detailed analysis of the conditions under which these processes return to a prescribed compact region in finite time. It also explores the interplay between continuous and discrete components in dynamic systems, offering practical examples and rigorous mathematical proofs. The chapter concludes with a discussion on the implications of these findings for various applications, making it a comprehensive guide for professionals in the field of stochastic processes and dynamic systems.
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previous chapter Switching Diffusion
next chapter Ergodicity
Title
Recurrence
Authors
Hai-Dang Nguyen
George Yin
Chao Zhu
Copyright Year
2025
Book
Hybrid Switching Diffusions

Print ISBN: 978-3-031-93302-8

Electronic ISBN: 978-3-031-93303-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-93303-5_3
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