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.
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页码：905 / 924
页数：20
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