School of Mathematics, Shandong University, Jinan 250100, China.
School of Mathematical Sciences, Fudan University, Shanghai 200433, China.
Chaos. 2023 Feb;33(2):023109. doi: 10.1063/5.0135471.
In this paper, we consider a distributed-order fractional stochastic differential equation driven by Lévy noise. We, first, prove the existence and uniqueness of the solution. A Euler-Maruyama (EM) scheme is constructed for the equation, and its strong convergence order is shown to be min{1-α,0.5}, where α depends upon the weight function. Besides, we present a fast EM method and also the error analysis of the fast scheme. In addition, several numerical experiments are carried out to substantiate the mathematical analysis.
本文考虑了由 Lévy 噪声驱动的分布阶分数随机微分方程。我们首先证明了该方程解的存在唯一性。针对该方程构造了一个 Euler-Maruyama (EM) 格式，并证明了其强收敛阶为 min{1-α,0.5}，其中α依赖于权函数。此外，我们还提出了一种快速 EM 方法，并对快速格式进行了误差分析。此外，还进行了一些数值实验以验证数学分析的正确性。
