Intermediate spaces, Gaussian probabilities and exponential tightness

Paolo Baldi

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arXiv · 2103.10758

Intermediate spaces, Gaussian probabilities and exponential tightness

Paolo Baldi

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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.

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Paolo Baldi. 2021-03-19. Intermediate spaces, Gaussian probabilities and exponential tightness. https://arxiv.org/abs/2103.10758

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