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Central limit theorem for a Gaussian incompressible flow with additional Brownian noise

Miernowski T.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

413--434

We generalize the result of Komorowski and Papanicolaou published in [7]. We consider the solution of stochastic differential equation dX (t) = V (t, X(t)) dt + √2κdB(t), where B(t) is a standard d-dimensional Brownian motion and V (t, x), (t, x) ∈ R × Rd, is a d-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as ε ↓ 0 of the family of rescaled processes Xε(t) = εX(t/ε2) exists and may be identified as a certain Brownian motion.