Chasing balls through martingale fields
成果类型：
Article
署名作者：
Scheutzow, M; Steinsaltz, D
署名单位：
Technical University of Berlin; University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
2046-2080
关键词：
摘要：
We consider the way sets are dispersed by the action of stochastic flows derived from martingale fields. Under fairly general continuity and ellipticity conditions, the following dichotomy result is shown: any nontrivial connected set X either contracts to a point under the action of the flow, or its diameter grows linearly in time, with speed at least a positive deterministic constant Lambda. The linear growth may further be identified (again, almost surely), with a much stronger behavior, which we call ball-chasing: if psi is any path with Lipschitz constant smaller than Lambda, the ball of radius epsilon around psi (t) contains points of the image of X for an asymptotically positive fraction of times t. If the ball grows as the logarithm of time, there are individual points in X whose images eventually remain in the ball.