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Some Asymptotic Formulae for Gaussian Distributions


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  • Yurinsky, V. V.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 2 (February)
    Pages: 303-332

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:303-332

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    Keywords: Gaussian distribution Hilbert space Gramer transformation Laplace method large deviations (null);


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