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5. Numerical Approximation

  • 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 numerical approximation methods for switching diffusions where the switching component is x-dependent, addressing the complexities of coupling continuous states and discrete events. It introduces Euler's scheme for approximating solutions and provides a detailed analysis of the convergence and rates of convergence of these algorithms. The chapter includes practical examples to illustrate the application of these methods and offers remarks on Markovian switching diffusions and truncation algorithms. Additionally, it discusses the challenges of numerical finite explosion times and presents a class of projection/truncation algorithms to mitigate these issues. The chapter concludes with a discussion on the broader context of numerical methods for stochastic differential equations and the potential for future research in this area.
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previous chapter Ergodicity
next chapter Stability
Title
Numerical Approximation
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_5
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