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Contents of PMS, Vol. 2, Fasc. 1,
pages 1 - 29
 

ÉVALUATIONS DE CERTAINES FONCTIONNELLES ASSOCIÉES À DES FONCTIONS ALÉATOIRES GAUSSIENNES

X. Fernique

Abstract: Let X = (X(w, t),w (- _O_,t (- T ) be a random function on (_O_,a,P), let T be a finite set, and m a probability on T. We assume that the components of X are P -integrable. We denote by M(m) the set of the random probabilities m = (m(w), w (- _O_) on T whose expectation is m. We put

integral f(X, m) = m(s - Mu(pm) E[ T X(w,t)m(w,dt)].

In this paper, we extend and study this quantity when T is in fact a Polish space (Section 1); then we show (Section 2) that if X is Gaussian and rather regular, then f(X,m) is monotonic in terms of the metric defined by X (Theorem 2.1), finally (Section 3), we majorize (Theorem 3.1) or minorize (3.2) the function f(X, m) in some cases.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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