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1. Introduction and Motivation

  • 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 introduces the concept of switching diffusion processes, which combine continuous dynamics with discrete events. It begins by addressing the motivations behind studying these hybrid systems and provides an overview of their properties and applications. The chapter then delves into various examples, such as the Lotka–Volterra model in ecological population dynamics, balanced realizations in control systems, and financial engineering applications. It also explores the stability, ergodicity, and numerical approximations of these processes. Additionally, the chapter discusses the invariance principle, models with Lévy jumps, and applications in mathematical biology. The text concludes with an appendix containing mathematical preliminaries and notes on related topics. Readers will gain a deep understanding of switching diffusion processes and their significance in various fields, as well as insights into recent advancements and challenges in the field.
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next chapter Switching Diffusion
Title
Introduction and Motivation
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_1
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