ASYMPTOTIC SUPPORT THEOREM FOR PLANAR ISOTROPIC BROWNIAN FLOWS

• 成果类型: Article
• 署名作者: Biskamp, Moritz
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP701
• 发表日期: 2013
• 页码: 699-721
• 关键词: stochastic dispersion

摘要

It has been shown by various authors that the diameter of a given nontrivial bounded connected set X grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In case of a planar IBF with a positive top-Lyapunov exponent, the precise deterministic linear growth rate K of the diameter is known to exist. In this paper we will extend this result to an asymptotic support theorem for the time-scaled trajectories of a planar IBF phi, which has a positive top-Lyapunov exponent, starting in a nontrivial compact connected set X subset of R-2; that is, we will show convergence in probability of the set of time-scaled trajectories in the Hausdorff distance to the set of Lipschitz continuous functions on [0, 1] starting in 0 with Lipschitz constant K.