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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 23, Fasc. 2,
pages 413 - 434
 

CENTRAL LIMIT THEOREM FOR A GAUSSIAN INCOMPRESSIBLE FLOW WITH ADDITIONAL BROWNIAN NOISE

Tomasz Miernowski

Abstract: 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+ V~ 2kdB(t),
where B(t) is a standard d -dimensional Brownian motion and V(t,x),(t,x) (- R ŚRd , is a d -dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as e |, 0 of the family of rescaled processes Xe(t) = eX(t/e2) 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.

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