Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

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{αm−αm−1,αm−0.5} with 0 < α 1 < α 2 < ⋯ < α m−1 < α m < 1, α m > 0.5, and m is a given positive integer. Finally, three numerical examples are provided to support our theoretical findings.