Simulating diffusion bridges using the Wiener chaos expansion

In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of t...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Delgado-Vences, Francisco, Gabriel Adrián Salcedo-Varela, Baltazar-Larios, Fernando
Format: Article
Language:English
Subjects:
Differential equations
Diffusion rate
Ornstein-Uhlenbeck process
Rejection rate
Simulation
Statistical inference
Online Access:Get full text
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Summary:In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of the diffusion bridge. Thus, we obtain a method to simulate the proposal diffusion bridges that is fast and that in every attempt constructs a diffusion bridge, which means there are no rejection rates. The method presented in this work could be very useful in statistical inference. We validate the method with a simple Ornstein-Uhlenbeck process. We apply our method to three examples of SDEs and show the numerical results.
ISSN:2331-8422