The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion. (English) Zbl 1154.60046

Authors’ abstract: 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 \(O(\delta ^{2H-1})\) , where \(\delta \) is the diameter of partition used for discretization. For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is \(O(\delta^H)\) .


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G18 Self-similar stochastic processes
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