Sample path properties of the stochastic flows

• 成果类型: Article
• 署名作者: Dolgopyat, D; Kaloshin, V; Koralov, L
• 署名单位: University System of Maryland; University of Maryland College Park; California Institute of Technology; Princeton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 1-27
• 关键词: statistical equilibrium; random transformations; Brownian motions; dispersion; diffeomorphisms; dimension; entropy; FORMULA

摘要

We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi-point motion.