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8. Invariance Principles

  • 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 focuses on the invariance principles of switching diffusion processes, building upon previous studies of stability in switching diffusions and random switching ordinary differential equations. It provides a comprehensive analysis of the long-term behavior of these processes, using Lyapunov function-type criteria and sample paths to derive invariance principles. The chapter also examines linear systems and their stability, offering insights into the dynamics of these complex systems. Key topics include the formulation of the problem, the use of sample paths and kernels of associated Lyapunov functions, and the stability of invariant sets. The chapter concludes with a discussion on the practical applications and theoretical implications of these findings, making it a valuable resource for professionals interested in the stability and long-term behavior of switching diffusion processes.
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previous chapter Stability of Switching ODEs
next chapter Two-Time-Scale Switching Diffusions
Title
Invariance Principles
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_8
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