Fermeture en probabilité de certains sous-espaces d'un espace L 2

Summary Let _i , iI be a family of equidistributed, independant random variables, defined on a probability space (, , P). Let {f _m , mN{ be a sequence of functions such that the f _m ( _i ) are, for every i, centered random variables in L ²(, , P) and in an L _p (, , P) (where p is an even integer at least equal to 4).In this paper the closed linear subspaces of L ² (, , P) generated by the variables of the form , where for fixed M, are studied. A uniform bound of the L ^p norm of elements of the unit ball of the above defined subspaces and also the closure in probability of these subspaces is thus obtained. These results are applied to Wiener's chaos of gaussian variables.

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Equipe de Recherche n⁰ 1 « Processus stochastiques et applications » dépendant de la Section n⁰ 2 «Théories Physiques et Probabilités », associée au C.N.R.S.