On a type of stochastic differential equations driven by countably many Brownian motions

被引：36

作者：

Cao, GL ^{[1
]}

He, K ^{[1
]}

机构：

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 203卷 / 01期

关键词：

one-dimensional SDE; existence; uniqueness; non-contact property; strong comparison theorem;

D O I：

10.1016/S0022-1236(03)00066-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the one-dimensional SDE X-t = x+ Sigma(i=1)(infinity) integral(0)(1)sigma(i)(X-s) dW(s)(i) + integral(0)(1)b(X-s) ds, where W-i is an infinite sequence of independent standard Brownian motions, i = 1, 2, 3,... . We prove two theorems on the existence and uniqueness of solutions with non-Lipschitz coefficients, and give a non-contact property and a strong comparison theorem for solutions. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：262 / 285

页数：24

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