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

Mishura, Yu; Shevchenko, G.

Stochastics 80, No. 5, 489-511 (2008).

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 \(O(\delta^H)\) .

Reviewer: Stanisław Wedrychowicz (Rzeszów)

MSC:

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

Keywords:

Euler approximations; stochastic differential equations; fractional Brownian motion; fractional white noise; rate of convergence

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