Strong Convergence of a Modified Euler-Maruyama Method for Mixed Stochastic Fractional Integro-Differential Equations with Local Lipschitz Coefficients

doi:10.3390/fractalfract9050296

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	Strong Convergence of a Modified Euler-Maruyama Method for Mixed Stochastic Fractional Integro-Differential Equations with Local Lipschitz Coefficients
	Yang, Zhaoqiang1,2 ; Xu, Chenglong 1
	2025-05-01
发表期刊	FRACTAL AND FRACTIONAL
卷号	9 期号:5
摘要	This paper presents a modified Euler-Maruyama (EM) method for mixed stochastic fractional integro-differential equations (mSFIEs) with Caputo-type fractional derivatives whose coefficients satisfy local Lipschitz and linear growth conditions. First, we transform the mSFIEs into an equivalent mixed stochastic Volterra integral equations (mSVIEs) using a fractional calculus technique. Then, we establish the well-posedness of the analytical solutions of the mSVIEs. After that, a modified EM scheme is formulated to approximate the numerical solutions of the mSVIEs, and its strong convergence is proven based on local Lipschitz and linear growth conditions. Furthermore, we derive the modified EM scheme under the same conditions in the L2 sense, which is consistent with the strong convergence result of the corresponding EM scheme. Notably, the strong convergence order under local Lipschitz conditions is inherently lower than the corresponding order under global Lipschitz conditions. Finally, numerical experiments are presented to demonstrate that our approach not only circumvents the restrictive integrability conditions imposed by singular kernels, but also achieves a rigorous convergence order in the L2 sense.
关键词	mixed stochastic fractional integro-differential equations fractional calculus mixed stochastic Volterra integral equation modified Euler-Maruyama method convergence rate analysis
DOI	10.3390/fractalfract9050296
收录类别	SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:001496045900001
出版者	MDPI
原始文献类型	Article
EISSN	2504-3110
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/39288
专题	图书馆
通讯作者	Yang, Zhaoqiang
作者单位	1.Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China; 2.Lanzhou Univ Finance & Econ, Lib & Sch Finance, Lanzhou 730101, Peoples R China
第一作者单位	兰州财经大学
通讯作者单位	兰州财经大学
推荐引用方式 GB/T 7714	Yang, Zhaoqiang,Xu, Chenglong. Strong Convergence of a Modified Euler-Maruyama Method for Mixed Stochastic Fractional Integro-Differential Equations with Local Lipschitz Coefficients[J]. FRACTAL AND FRACTIONAL,2025,9(5).
APA	Yang, Zhaoqiang,&Xu, Chenglong.(2025).Strong Convergence of a Modified Euler-Maruyama Method for Mixed Stochastic Fractional Integro-Differential Equations with Local Lipschitz Coefficients.FRACTAL AND FRACTIONAL,9(5).
MLA	Yang, Zhaoqiang,et al."Strong Convergence of a Modified Euler-Maruyama Method for Mixed Stochastic Fractional Integro-Differential Equations with Local Lipschitz Coefficients".FRACTAL AND FRACTIONAL 9.5(2025).