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

Jingjun Zhao Jingjun Zhao, Hao Zhou, Yang Xu

Type: Article

Publication Date: 2023-10-13

Citations: 1

DOI: https://doi.org/10.4208/jcm.2301-m2022-0088

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.

Locations

Journal of Computational Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients	2014	Chao Yue Chengming Huang
+	Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments	2016	Yulan Lu Minghui Song M.Z. Liu
+ PDF Chat	Exponential mean-square stability of two classes of theta Milstein methods for stochastic delay differential equations	2017	Omid Farkhondeh Rouz Davood Ahmadian Mariyan Milev
+	The improved split-step backward Euler method for stochastic differential delay equations	2011	Xiaojie Wang Siqing Gan
+ PDF Chat	The improved split-step backward Euler method for stochastic differential delay equations	2011	Xiaojie Wang Siqing Gan
+ PDF Chat	The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations	2022	Yu Zhang Enying Zhang Longsuo Li
+	Convergence and stability of split-step theta methods with variable step-size for stochastic pantograph differential equations	2017	Yu Xiao Mahmoud A. Eissa Boping Tian
+	Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems	2021	Ali Reza Soheili Yasser Taherinasab Mohammad Amini
+	Mean square stability of the split-step theta method for non-linear time-changed stochastic differential equations	2023	Dongxuan Wu Zhi Li Liping Xu Chuanhui Peng
+	Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability	2019	Linna Liu Haoyi Mo Feiqi Deng
+ PDF Chat	Convergence Rate of the Diffused Split-Step Truncated Euler–Maruyama Method for Stochastic Pantograph Models with Lévy Leaps	2023	Amr Abou-Senna Ghada AlNemer Yongchun Zhou Boping Tian
+	High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients	2016	Chao Yue
+	Strong convergence of split-step theta methods for non-autonomous stochastic differential equations	2014	Chao Yue Chengming Huang Fengze Jiang
+	Mean square stability of two classes of theta method for neutral stochastic differential delay equations	2016	Linna Liu Quanxin Zhu
+	Mean Square Stability and Dissipativity of Split-Step Theta Method for Stochastic Delay Differential Equations with Poisson White Noise Excitations	2016	Haiyan Yuan Jihong Shen Cheng Song
+	Mean square stability and dissipativity of two classes of theta methods for systems of stochastic delay differential equations	2013	Chengming Huang
+	Split-step forward methods for stochastic differential equations	2009	Peng Wang Yong Li
+	Convergence and stability of two classes of theta-Milstein schemes for stochastic differential equations	2015	Xiaofeng Zong Fuke Wu Gui‐Ping Xu
+	Truncated Euler–Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient	2023	Jie He Shuaibin Gao Weijun Zhan Qian Guo
+	Stability Analysis of Split‐Step θ$$ \theta $$‐Milstein Scheme for Stochastic Delay Integro‐Differential Equations	2024	Linna Liu Shixiang Zhou Jianyin Fang

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (10)

Action	Title	Year	Authors
+	Exponential mean square stability of numerical methods for systems of stochastic differential equations	2012	Chengming Huang
+ PDF Chat	Almost Sure Exponential Stability in the Numerical Simulation of Stochastic Differential Equations	2015	Xuerong Mao
+	Numerical simulation of stochastic ordinary differential equations in biomathematical modelling	2003	Margherita Carletti Kevin Burrage Pamela Burrage
+ PDF Chat	Convergence of delay differential equations driven by fractional Brownian motion	2010	Marco Ferrante Carles Rovira
+	Convergence rates of full-implicit truncated Euler–Maruyama method for stochastic differential equations	2018	Haining Wen
+	Moment estimates and applications for SDEs driven by fractional Brownian motions with irregular drifts	2021	Xiliang Fan Shao‐Qin Zhang
+	Integral and Discrete Inequalities and Their Applications	2016	Yuming Qin
+ PDF Chat	The Malliavin Calculus and Related Topics	1995	David Nualart
+ PDF Chat	Multi-level Monte Carlo methods with the truncated Euler–Maruyama scheme for stochastic differential equations	2017	Qian Guo Wei Liu Xuerong Mao Weijun Zhan
+	Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion	2019	Jialin Hong Chuying Huang Minoo Kamrani Xu Wang