Global flows for stochastic differential equations without global Lipschitz conditions
成果类型：
Article
署名作者：
Fang, Shizan; Imkeller, Peter; Zhang, Tusheng
署名单位：
Universite Bourgogne Europe; Humboldt University of Berlin; University of Manchester
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000412
发表日期：
2007
页码：
180-205
关键词：
摘要：
We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius R, are supposed to grow not faster than log R, while those of the diffusion vector fields are supposed to grow not faster than root log R. We regularize the stochastic differential equations by associating with them approximating ordinary differential equations obtained by discretization of the increments of the Wiener process on small intervals. By showing that the flow associated with a regularized equation converges uniformly to the solution of the stochastic differential equation, we simultaneously establish the existence of a global flow for the stochastic equation under local Lipschitz conditions.