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 fis defined on a locally convex space Xand 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 >0w.r.t. any Radon Gaussian measure on a nuclear space X, if pand qare continuous seminorms on Xwith compatible kernels. This can be viewed as an adaptation of Fernique’s theorem and, for example, has applications in quantum field theory.
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