Non-Lipschitz stochastic differential equations driven by multi-parameter Brownian motions

被引：17

作者：

Zhang, Xicheng ^{[1
]}

Zhu, Jingyang ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2006年 / 6卷 / 03期

基金：

美国国家科学基金会;

关键词：

Bihari's inequality; non-Lipschitz; stochastic differential equation; multiparameter Brownian motions; discretizing approximation;

D O I：

10.1142/S021949370600175X

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：

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L-2-convergence speeds.

引用

页码：329 / 340

页数：12

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