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Sample path properties of the stochastic flows

Dmitry Dolgopyat·Vadim Kaloshin·Leonid Koralov
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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 multipoint motion.

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Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov. 2002-05-03. Sample path properties of the stochastic flows. https://arxiv.org/abs/math/0111011

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