Euler-Maruyama and Milstein approximations for stochastic functional differential equations with distributed memory term

Abstract

We consider the problem of strong approximations of the solution of stochastic functional differential equations of Itô form with a distributed delay term in the drift and diffusion coefficient. We provide necessary background material, and give convergence proofs for the Euler-Maruyama and the Milestein scheme. Numerical examples illustrate the theoretical results