CENTRAL LIMIT THEOREM FOR A GAUSSIAN INCOMPRESSIBLE
FLOW WITH ADDITIONAL BROWNIAN NOISE
Abstract: We generalize the result of Komorowski and Papanicolaou published in [7]. We
consider the solution of stochastic differential equation

where

is a standard

-dimensional Brownian motion and

,
is a

-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite
time. We prove that the weak limit as

of the family of rescaled processes

exists and may be identified as a certain Brownian motion.
2000 AMS Mathematics Subject Classification: 60F05 (60G15).
Key words and phrases: Weak convergence, random process, Gaussian field,
incompressible flow, diffusion.