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.
"Sample path properties of the stochastic flows." Ann. Probab. 32 (1A) 1 - 27, January 2004. https://doi.org/10.1214/aop/1078415827