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

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.