Mathematics – Probability
Scientific paper
2007-05-12
Mathematics
Probability
21 pages, (incorrect) weak convergence result removed, to appear in Stochastics
Scientific paper
10.1080/17442500802024892
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 $O(\delta^H)$.
Mishura Yuliya
Shevchenko Georgiy
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