Super-Gaussian decay of exponentials: A sufficient condition

In this article, we present a sufficient condition for the exponential exp⁡(−f) to have a tail decay stronger than any Gaussian, where f is defined on a locally convex space X and grows faster than a squared seminorm on X. In particular, our result proves that exp⁡(−p(x)2+ε+αq(x)2) is integrable for...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-12, Vol.528 (1), p.127558, Article 127558
Main Authors: Hinrichs, Benjamin, Janssen, Daan W., Ziebell, Jobst
Format: Article
Language:English
Subjects:
Fernique's theorem
Locally convex spaces
Radon Gaussian measures
Super-Gaussian decay
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we present a sufficient condition for the exponential exp⁡(−f) to have a tail decay stronger than any Gaussian, where f is defined on a locally convex space X and grows faster than a squared seminorm on X. In particular, our result proves that exp⁡(−p(x)2+ε+αq(x)2) is integrable for all α,ε>0 w.r.t. any Radon Gaussian measure on a nuclear space X, if p and q are continuous seminorms on X with compatible kernels. This can be viewed as an adaptation of Fernique's theorem and, for example, has applications in quantum field theory.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127558