95-07

On Distribution of Quadratic Forms in Gaussian Random Variables

by Christoph, G.; Prohorov,Yu.V.; Ulyanov, V. V.

 

Preprint series: 95-07, Preprints

The paper is published: Teor. Veroyatn. Primen. 40 (1995), No.2, 301-312 (Russian original)\rEnglish translation in\rTheory Probab. Appl. 40 (1995), No.2, 250-260

MSC:
60B11 Probability theory on linear topological spaces, See Also { 28C20}
60G15 Gaussian processes
60F10 Large deviations

 

Abstract: Two-sided bounds are constructed for a density function p(u; a) of a ran-dom variable |Y - a|^2 , where Y is a Gaussian random element in a Hilbertspace with zero mean. The estimates are sharp in the sense that starting fromlarge enough u the ratio of upper bound to lower bound equals 8 and doesnot depend on any parameters of a distribution of |Y - a|^2 . The estimatesimply two-sided bounds for probabilities P (|Y - a| > r).


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