The rate of convergence of Euler approximations for solutions of stochastic differential equations driven by fractional Brownian motion

Yuliya Mishura, Georgiy Shevchenko

Published 2007-05-12, updated 2008-02-14Version 2

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index $H>1/2$ can be estimated by $O(\delta^{2H-1})$ ($\delta$ is the diameter of partition). For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is $O(\delta^H)$.