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Sample path properties of the stochastic flows

Dolgopyat, Dmitry and Kaloshin, Vadim and Koralov, Leonid (2004) Sample path properties of the stochastic flows. Annals of Probability, 32 (1A). pp. 1-27. ISSN 0091-1798. http://resolver.caltech.edu/CaltechAUTHORS:DOLaop04

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Abstract

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.


Item Type:Article
Additional Information:© 2004 The Institute of Mathematical Statistics Received October 2001; revised October 2002. [DD] Supported in part by the NSF and Sloan Foundation. [VK] Supported in part by American Institute of Mathematics fellowship and Courant Institute. [LK] Supported in part by an NSF postdoctoral fellowship. This paper was started during the conference Nonlinear Analysis, 2000. D. Dolgopyat is grateful to IMA for the travel grant to attend this conference. During the work on this paper we enjoyed the hospitality of IMPA, Rio de Janeiro and of Universidad Autonoma de Madrid. We are especially grateful to J. Palis, M. Viana, A. Cordoba and D. Cordoba for providing excellent working conditions in Rio de Janeiro and Madrid. The authors would like to thank P. Friz and S. R. S. Varadhan for useful comments. We are also grateful to P. Baxendale and the anonymous referee for constructive criticism on the original version of this paper.
Subject Keywords:Lyapunov exponents; stochastic flows; random diffeomorphisms; central limit theorems; passive scalar
Record Number:CaltechAUTHORS:DOLaop04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:DOLaop04
Alternative URL:http://dx.doi.org/10.1214/aop/1078415827
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3092
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:15 May 2006
Last Modified:26 Dec 2012 08:52

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