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Volume 42, Issue 5
Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion

Jingjun Zhao, Hao Zhou & Yang Xu

DOI: 10.4208/jcm.2301-m2022-0088

J. Comp. Math., 42 (2024), pp. 1226-1245.

Published online: 2024-07

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  • 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.

  • Keywords

Stochastic differential equation, Fractional Brownian motion, Split-step theta method, Strong convergence, Exponential stability.

  • AMS Subject Headings

65L20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-1226, author = {Zhao , JingjunZhou , Hao and Xu , Yang}, title = {Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2301-m2022-0088}, url = {http://global-sci.org/intro/article_detail/jcm/23276.html} }
TY - JOUR T1 - Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion AU - Zhao , Jingjun AU - Zhou , Hao AU - Xu , Yang JO - Journal of Computational Mathematics VL - 5 SP - 1226 EP - 1245 PY - 2024 DA - 2024/07 SN - 42 DO - http://doi.org/10.4208/jcm.2301-m2022-0088 UR - https://global-sci.org/intro/article_detail/jcm/23276.html KW - Stochastic differential equation, Fractional Brownian motion, Split-step theta method, Strong convergence, Exponential stability. AB -

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.

Zhao , JingjunZhou , Hao and Xu , Yang. (2024). Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion. Journal of Computational Mathematics. 42 (5). 1226-1245. doi:10.4208/jcm.2301-m2022-0088
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