Some Asymptotic Formulae for Gaussian Distributions

V. V. Yurinsky

Journal of Multivariate Analysis, 1996, vol. 56, issue 2, 303-332

Abstract: This paper considers asymptotic expansions of certain expectations which appear in the theory of large deviation for Gaussian random vectors with values in a separable real Hilbert space. A typical application is to calculation of the "tails" of distributions of smooth functionals,p(r)=P{[Phi](r-1[xi])[greater-or-equal, slanted]0},r-->[infinity], e.g., the probability that a centered Gaussian random vector hits the exterior of a large sphere surrounding the origin. The method provides asymptotic formulae for the probability itself and not for its logarithm in a situation, where it is natural to expect thatp(r)=c'rDÂ exp{-c''r2}. Calculations are based on a combination of the method of characteristic functionals with the Laplace method used to find asymptotics of integrals containing a fast decaying function with "small" support.

Keywords: Gaussian; distribution; Hilbert; space; Gramer; transformation; Laplace; method; large; deviations; (null) (search for similar items in EconPapers)
Date: 1996
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