• 论文 •

### 非线性随机分数阶微分方程Euler方法的弱收敛性

1. 湘潭大学科学工程计算与数值仿真湖南省重点实验室, 湘潭 411105
• 收稿日期:2019-04-18 出版日期:2021-02-15 发布日期:2021-02-04
• 基金资助:
国家自然科学基金（12071403）和湖南省教育厅重点项目（18A049）资助.

Zhu Mengjiao, Wang Wenqiang. THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(1): 87-109.

### THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

Zhu Mengjiao, Wang Wenqiang

1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105 China
• Received:2019-04-18 Online:2021-02-15 Published:2021-02-04

This paper is concerned with the existence and uniqueness of solutions for nonlinear stochastic fractional differential equations and the weak convergence of Euler method constructed for solving the equations when they satisfy certain constraints. Especially, when fractional order α = 0, the equations are degenerated to nonlinear stochastic differential equations, and the conclusions obtained from this paper are consisted with the relevant results; when α ≠ 0 and the initial condition is homogeneous, the conclusions can be regarded as the generalization and improvement of linear stochastic fractional differential equations in the existing literature. Finally, numerical examples illustrate the effectiveness of the theoretical results.

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