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

被引：45

作者：

Mishura, Yu ^{[1
]}

Shevchenko, G. ^{[1
]}

机构：

[1] Kyiv Natl Taras Shevchenko Univ, Dept Mech & Math, UA-01033 Kiev, Ukraine

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2008年 / 80卷 / 05期

关键词：

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

D O I：

10.1080/17442500802024892

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Skorohodtype quasilinear equation driven by fBm we prove that the rate of convergence is O(delta(H)).

引用

页码：489 / 511

页数：23

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