Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes

Abstract

We consider the Euler approximation of stochastic differential equations (SDEs) driven by Lévy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y= Z( V) with V a subordinator and Z a stable process, we propose an approximation Y by Z( V n ) where V n is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs.