Convergence and Stability of an Explicit Method for Autonomous Time-Changed Stochastic Differential Equations with Super-Linear Coefficients
Year: 2023
Author: Xiaotong Li, Juan Liao, Wei Liu, Zhuo Xing
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 651–683
Abstract
In this paper, numerical methods for the time-changed stochastic differential equations of the form $$d\Upsilon(t)=a(\Upsilon(t))dt+b(\Upsilon(t))dE(t)+\sigma(\Upsilon(t))dB(E(t))$$ are investigated, where all the coefficients $a(·),$ $b(·)$ and $\sigma(·)$ are allowed to contain some super-linearly growing terms. An explicit method is proposed by using the idea of truncating terms that grow too fast. Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained. The proposed method is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense. Simulations are provided to demonstrate the theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0335
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 651–683
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Time-changed stochastic differential equations explicit method super-linear coefficients strong convergence asymptotic stability.