Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion

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.

Author Details

Jingjun Zhao

Hao Zhou

Yang Xu