A modified Euler–Maruyama method for Riemann–Liouville stochastic fractional integro-differential equations. Issue 2 (22nd January 2023)

• Record Type: Journal Article
• Authors: Zheng, Yu; Qian, Siying; Arshad, Sadia; Huang, Jianfei
• Is Part Of: Journal of statistical computation and simulation. Volume 93:Issue 2(2023)
• Page Start: 249
• Page End: 265
• Publication Date: 2023-01-22
• Subjects: Stochastic fractional integro-differential equations -- weakly singular kernels -- modified Euler–Maruyama method -- convergence; 60H10 -- 65C30; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2022.2100889
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : In this paper, we propose a modified Euler–Maruyama (EM) method for Riemann–Liouville stochastic fractional integro-differential equations with weakly singular kernels, and then analyse the strong convergence of the proposed EM method. Specifically, we transform the considered stochastic fractional integro-differential equation into its equivalent form of stochastic Volterra integral equations and derive the corresponding modified EM method. Then, the strong convergence 1 − α order of the proposed method is established, where α is the order of Riemann–Liouville fractional derivative with 0 < α < 1 . Finally, numerical experiments are demonstrated to support our theoretical results.