Sample path properties of the stochastic flows

Dmitry Dolgopyat ^[3] ; Vadim Kaloshin ^[1] ; Leonid Koralov ^[2]
1. [1] California Institute of Technology
  
  California Institute of Technology
  
  Estados Unidos
2. [2] Princeton University
  
  Princeton University
  
  Estados Unidos
3. [3] University of Maryland
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Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 1, 2004, págs. 1-27
Idioma: inglés
DOI: 10.1214/aop/1078415827
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Resumen
- 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.