2024
DOI: 10.1088/1402-4896/ad1cba
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Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

Jianfei Huang,
Linxin Shao,
Jiahui Liu

Abstract: In this paper, we first prove the existence, uniqueness and continuity dependence on the initial value of multi-term Caputo tempered fractional stochastic differential equations with initial value. Then, an Euler-Maruyama (EM) method is presented for solving the considered equation. The strong convergence of the presented EM method is strictly investigated with the order to be $\min\{\alpha_m-\alpha_{m-1},\alpha_{m}-0.5\}$ with $0<\alpha_{1}<\alpha_{2}<\cdots<\alpha_{m-1}<\alpha_{m}<1$, $\alp… Show more

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