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6. Stability

  • 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 stability analysis of switching diffusion processes, focusing on the use of Lyapunov function methods to understand the stability of nonlinear systems through their linearized counterparts. The text begins with an introduction to the problem and the importance of linearization techniques, followed by a detailed formulation of the problem and auxiliary results. Key topics include stability and instability in probability, p-stability and exponential p-stability, and almost sure exponential stability. The chapter also provides necessary and sufficient conditions for exponential p-stability and discusses the stability and instability of linearized systems. Practical examples, such as the Lot-Volterra model, illustrate the theoretical concepts. The chapter concludes with a discussion on the framework and new results derived from recent research, offering a comprehensive guide to stability analysis in switching diffusion processes.
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previous chapter Numerical Approximation
next chapter Stability of Switching ODEs
Title
Stability
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_6
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