Uniqueness of Solutions of Stochastic Differential Equations

被引：70

作者：

Davie, A. M. ^{[1
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2007年 / 2007卷

关键词：

D O I：

10.1093/imrn/rnm124

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the stochastic differential equation dx(t) = dW(t) + f (t, x(t)) dt, x(0) = x(0) for t >= 0, where x(t) is an element of R-d, W is a standard d-dimensional Brownian motion, and f is a bounded Borel function from [0,infinity) x R-d to R-d. We show that, for almost all Brownian paths W(t), there is a unique x(t) satisfying this equation.

引用

页数：26