The admissible mean values of a stochastic process

Abstract

Px+g+f < Px+gif and only if Px+f < Px. We will also assume that the correlation function R(s,t) = fx(s)x(t)Px(dx) satisfies fT fTR2(s, t)dsdt < oo so that the integral transform R: Rf (s) = fTR(s, t)f (t)dt is a compact operator on L2(T). EXAMPLE 1. If x(t) is a Gaussian process with continuous sample functions, then M(x)= R1,2(L2(T)) (where for each f in R/2(L2(t)) its continuous version