Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift

被引：23

作者：

Kohatsu-Higa, Arturo ^{[1
]}

Lejay, Antoine ^{[2
,3
,4
]}

Yasuda, Kazuhiro ^{[5
]}

机构：

[1] Ritsumeikan Univ, Dept Math Sci, 1-1-1 Nojihigashi, Kusatsu, Shiga 5258577, Japan

[2] Japan Sci & Technol Agcy, 1-1-1 Nojihigashi, Kusatsu, Shiga 5258577, Japan

[3] Univ Lorraine, IECL, UMR 7502, F-54500 Vandoeuvre Les Nancy, France

[4] CNRS, IECL, UMR 7502, F-54500 Vandoeuvre Les Nancy, France

[5] INRIA, F-54500 Villers Les Nancy, France

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 326卷

关键词：

Stochastic differential equation; Euler-Maruyama scheme; Discontinuous drift; Weak rate of convergence; Malliavin calculus; MALLIAVIN CALCULUS; APPROXIMATION; DIFFUSION; BOUNDS; SDES;

D O I：

10.1016/j.cam.2017.05.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an Euler-Maruyama type approximation method for a stochastic differential equation (SDE) with a non-regular drift and regular diffusion coefficient. The method regularizes the drift coefficient within a certain class of functions and then the Euler-Maruyama scheme for the regularized scheme is used as an approximation. This methodology gives two errors. The first one is the error of regularization of the drift coefficient within a given class of parametrized functions. The second one is the error of the regularized Euler -Maruyama scheme. After an optimization procedure with respect to the parameters we obtain various rates, which improve other known results. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：138 / 158

页数：21

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