Milstein's type schemes for fractional SDEs

被引：21

作者：

Gradinaru, Mihai ^{[1
]}

Nourdin, Ivan ^{[2
]}

机构：

[1] Univ Rennes 1, Inst Rech Math Rennes, F-35042 Rennes, France

[2] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 5, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2009年 / 45卷 / 04期

关键词：

Fractional Brownian motion; Weighted power variations; Stochastic differential equation; Milstein's type scheme; Exact rate of convergence; DIFFERENTIAL-EQUATIONS DRIVEN; APPROXIMATION; INTEGRALS;

D O I：

10.1214/08-AIHP196

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Weighted power variations of fractional Brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.

引用

页码：1085 / 1098

页数：14

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