Probability and Statistics Seminar: Exponential integrability for Gaussian measures

Friday, March 5 at 3:30pm to 4:30pm

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Paata Ivanisvili, North Carolina State

Abstract: Let X be the standard Gaussian random vector. In this talk I will discuss conditions on a real valued test function f such that the exponential integral E exp(f(X)) is finite. Talagrand showed that if the exponential of the square of the gradient of f divided by 2 is integrable with respect to the standard Gaussian measure then this guarantees  finiteness of E exp(f(X)). In the joint work with Ryan Russell we sharpen this result, and we also provide  quantitative dimension independent bounds relating these two quantities.

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