MITTAG-LEFFLER EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

Xiangting Hu; Aiguo Xiao; Xinjie Dai; Mengjie Wang

doi:10.11948/20250132

2026 Volume 16 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(2): 895-915

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Xiangting Hu, Aiguo Xiao, Xinjie Dai, Mengjie Wang. MITTAG-LEFFLER EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 895-915. doi: 10.11948/20250132

Citation:

Xiangting Hu, Aiguo Xiao, Xinjie Dai, Mengjie Wang. MITTAG-LEFFLER EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 895-915. doi: 10.11948/20250132

MITTAG-LEFFLER EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

1.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering & National Center for Applied Mathematics in Hunan & Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, 411105 Xiangtan City, China
2.
School of Mathematics and Statistics, Yunnan University, 650504 Kunming City, China

Author Bio: Email: 202221511168@smail.xtu.edu.cn(X. Hu); Email: xag@xtu.edu.cn(A. Xiao); Email: dxj@ynu.edu.cn(X. Dai)
Corresponding author: Email: mengjiewang@smail.xtu.edu.cn(M. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12471391, 12401547)

Abstract

Abstract

This paper reconsiders the linear stochastic Volterra integral equations with weakly singular kernels. For the equivalent form of the underlying equation, we propose the improved version of the existing mean-square asymptotical stability result for the exact solution. Moreover, some new or improved results are obtained for the Mittag-Leffler Euler–Maruyama method for the equations, and it is shown that the method shares sharp strong convergence with order $ 1/2-\beta $ and carries preferable stability. The numerical examples are performed to show the accuracy and effectiveness of the numerical scheme and verify the correctness of the theoretical analysis.
- Stochastic Volterra integral equations /
- weakly singular kernels /
- Mittag-Leffler Euler-Maruyama method /
- mean-square asymptotic stability /
- strong convergence
MSC: 60H20, 60H35, 65C30

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References

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