Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient

Abstract

In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) Xt=x0+∫0tb(s,Xs)ds+Lt,x0∈Rd,t∈[0,T], where the drift coefficient b:[0,T]×Rd→Rd is Hölder continuous in both time and space variables and the noise L=(Lt)0≤t≤T is a d-dimensional Lévy process. We provide the rate of convergence for the Euler–Maruyama approximation when L is a Wiener process or a truncated symmetric α-stable process with α∈(1,2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation.