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.
Publié le : 2004-01-14
Classification:
Lyapunov exponents,
stochastic flows,
random diffeomorphisms,
central limit theorems,
passive scalar,
37H15,
37A25,
37D25,
60F05,
60F10
@article{1078415827,
author = {Dolgopyat, Dmitry and Kaloshin, Vadim and Koralov, Leonid},
title = {Sample path properties of the stochastic flows},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 1-27},
language = {en},
url = {http://dml.mathdoc.fr/item/1078415827}
}
Dolgopyat, Dmitry; Kaloshin, Vadim; Koralov, Leonid. Sample path properties of the stochastic flows. Ann. Probab., Tome 32 (2004) no. 1A, pp. 1-27. http://gdmltest.u-ga.fr/item/1078415827/