Intermediate spaces, Gaussian probabilities and exponential tightness

2021/03/19 by Baldi, Paolo
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.10758

Abstract

Let us consider a Gaussian probability on a Banach space. We prove the existence of an intermediate Banach space between the space where the Gaussian measure lives and its RKHS. Such a space has full probability and a compact embedding. This extends what happens with Wiener measure, where the intermediate space can be chosen as a space of Hölder paths. From this result it is very simple to deduce a result of exponential tightness for Gaussian probabilities.

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