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Article Dans Une Revue Probability and Mathematical Statistics Année : 2003

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

Résumé

We generalize the result of T. Komorowski and G. Papanicolaou. We consider the solution of stochastic differential equation $dX(t)=V(t,X(t))dt+\sqrt{2\kappa}dB(t)$ where $B(t)$ is a standard $d$-dimensional Brownian motion and $V(t,x)$, $(t,x)\in R \times R^{d}$ is a $d$-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as $\ep\downarrow 0$ of the family of rescaled processes $X_{\epsilon}(t)=\epsilon X(\frac{t}{\epsilon^{2}})$ exists and may be identified as a certain Brownian motion.
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Dates et versions

hal-00020749 , version 1 (14-03-2006)

Identifiants

  • HAL Id : hal-00020749 , version 1

Citer

Tomasz Miernowski. Central limit theorem for a Gaussian incompressible flow with additional Brownian noise. Probability and Mathematical Statistics, 2003, 23 (2), pp.413-434. ⟨hal-00020749⟩

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