Abstract
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
{
α
m
−
α
m
−
1
,
α
m
−
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province of China
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics