ERROR ESTIMATES OF THE θ-SCHEME FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

被引：50

作者：

Zhao, Weidong ^{[1
]}

Wang, Jinlei ^{[1
]}

Peng, Shige ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2009年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

Backward stochastic differential equations; theta-scheme; Error estimate; QUASI-LINEAR PDES; NUMERICAL-METHOD; SDES; DISCRETIZATION; ALGORITHM;

D O I：

10.3934/dcdsb.2009.12.905

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the error estimate of the theta-scheme for the backward stochastic differential equation y(t) = phi(W(T)) + integral(T)(t) f(s, y(s))d(s) - integral(T)(t) z(s)dWs. We show that this scheme is of first-order convergence in y for general theta. In particular, for the case of theta = 1/2 (i.e., the Crank-Nicolson scheme), we prove that this scheme is of second-order convergence in y and first-order in z. Some numerical examples are also given to validate our theoretical results.

引用

页码：905 / 924

页数：20

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