Stochastic differential equation driven by countably many Brownian motions with non-Lipschitzian coefficients

被引：7
|
作者：
Liang, ZX [1 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2006年 / 24卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Euler approximation; large deviations principle; non-explosion; non-Lipschitzian; pathwise uniqueness;
D O I：
10.1080/07362990600629017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study m -dimensional SDE X-t = x(0) + Sigma(infinity)(i=1) integral(t)(0) sigma(i) (X-s) dW(s)(i) + integral(t)(0) b(X-s)ds, where {W-i)(i >= 1) is an infinite sequence of independent standard one-dimensional Brownian motions. Existence and pathwise uniqueness, non-explosion, and a Freidlin-Wentzell large deviations principle of strong solutions to the SDE are established under modulus of continuity of the coefficients is less than vertical bar x -y vertical bar (log(1)/((x - y)))(y), y epsilon [0, 1], which are different from that results constructed recently by Cao and He [2] and Fang and Zhang [6].
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页码：501 / 529
页数：29
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