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11. Past-Dependent Switching Diffusion

  • 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 explores the modeling, analysis, and computation of complex networked systems using hybrid diffusions, where switching rates depend on the past history of the continuous component. It introduces the concept of past-dependent switching diffusions and discusses their applications in various fields, including the LQG problem and queueing systems. The chapter covers the formulation and examples of switching diffusions, the existence and uniqueness of solutions, Markov and Feller properties, recurrence and ergodicity, and stability. It also provides Dupire’s functional Itô formula and discusses the stability and instability of linearized systems. The chapter concludes with examples and further remarks, offering a comprehensive overview of past-dependent switching diffusions and their practical implications.
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previous chapter Switching Jump Diffusions: Time-Scale Separations
next chapter Population Dynamics Modeled by Switching Diffusion
Title
Past-Dependent Switching Diffusion
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_11
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