Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9518819 | Bulletin des Sciences Mathématiques | 2005 | 16 Pages |
Abstract
We study m-dimensional SDE Xt=x0+âi=1ââ«0tÏi(Xs)dWsi+â«0tb(Xs)ds, where {Wi}i⩾1 is an infinite sequence of independent standard d-dimensional Brownian motions. The existence and pathwise uniqueness of strong solutions to the SDE was established recently in [Z. Liang, Stochastic differential equations driven by countably many Brownian motions with non-Lipschitzian coefficients, Preprint, 2004]. We will show that the unique strong solution produces a stochastic flow of homeomorphisms if the modulus of continuity of coefficients is less than |xây|(log1|xây|)Ï, Ïâ[0,1) with (â1)Ï=1, and the coefficients are compactly supported.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Zongxia Liang,