Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion
Year: 2024
Author: Jingjun Zhao, Hao Zhou, Yang Xu
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1226–1245
Abstract
For solving the stochastic differential equations driven by fractional Brownian motion, we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta method. For the problem under a locally Lipschitz condition and a linear growth condition, we analyze the strong convergence and the exponential stability of the proposed method. Moreover, for the stochastic delay differential equations with locally Lipschitz drift condition and globally Lipschitz diffusion condition, we give the order of convergence. Finally, numerical experiments are done to confirm the theoretical conclusions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2301-m2022-0088
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1226–1245
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stochastic differential equation Fractional Brownian motion Split-step theta method Strong convergence Exponential stability.