Intermediate spaces, Gaussian probabilities and exponential tightness
Probability
2021-03-22 v1
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 H\"older paths. From this result it is very simple to deduce a result of exponential tightness for Gaussian probabilities.
Keywords
Cite
@article{arxiv.2103.10758,
title = {Intermediate spaces, Gaussian probabilities and exponential tightness},
author = {Paolo Baldi},
journal= {arXiv preprint arXiv:2103.10758},
year = {2021}
}