2003 Prépublication d'Orsay numéro 2003-05 (06/05/2003)



LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM FOR RANDOMLY FORCED PDE'S.

SHIRIKYAN, Armen - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : Strong law of large numbers; Central limit theorem; Navier-Stokes system.

Classification MSC : 35Q30; 60F05; 60H15; 60J25.


Resumé :

Abstract :
We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for solutions are established and the corresponding rates of convergence are estimated. The proofs are based on the property of exponential mixing for the problem in question and some abstract SLLN and CLT for mixing-type Markov processes.

Article : Fichier Postscript
Contact : Armen.Shirikyan@math.u-psud.fr