A distributed-order fractional stochastic differential equation driven by Lévy noise: Existence, uniqueness, and a fast EM scheme

Jincheng Dong; Ning Du; Zhiwei Yang

doi:10.1063/5.0135471

A distributed-order fractional stochastic differential equation driven by Lévy noise: Existence, uniqueness, and a fast EM scheme

Chaos. 2023 Feb;33(2):023109. doi: 10.1063/5.0135471.

Authors

Jincheng Dong¹, Ning Du¹, Zhiwei Yang²

Affiliations

¹ School of Mathematics, Shandong University, Jinan 250100, China.
² School of Mathematical Sciences, Fudan University, Shanghai 200433, China.

PMID: 36859229
DOI: 10.1063/5.0135471

Abstract

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.