ÉVALUATIONS DE CERTAINES FONCTIONNELLES ASSOCIÉES À DESFONCTIONS ALÉATOIRES GAUSSIENNES
X. Fernique
Abstract: Let be a random function on let
be a finite set, and a probability on We assume that the components of
are -integrable. We denote by the set of the random probabilities
on whose expectation is We put
In this paper, we extend and study this quantity when is in fact a Polish space (Section
1); then we show (Section 2) that if is Gaussian and rather regular, then is
monotonic in terms of the metric defined by (Theorem 2.1), finally (Section
3), we majorize (Theorem 3.1) or minorize (3.2) the function in some
cases.