Sample path properties of the stochastic flows

By Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov. 2001

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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.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e72828f5a1da0982a2d17964f6ad478077db6950