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

摘要

The paper focuses on discrete-type approximations of solutions tonon-homogeneous stochastic differential equations (SDEs) involving fractionalBrownian motion (fBm). We prove that the rate of convergence for Eulerapproximations 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 ofpartition). For discrete-time approximations of Skorohod-type quasilinearequation driven by fBm we prove that the rate of convergence is $O(\delta^H)$.