On Distribution of Quadratic Forms in Gaussian Random Variables

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

Preprint series: 95-07, Preprints

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

MSC:
60B11 Probability theory on linear topological spaces, See Also {
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 Hilbert
space with zero mean. The estimates are sharp in the sense that starting from
large enough u the ratio of upper bound to lower bound equals 8 and does
not depend on any parameters of a distribution of |Y - a|^2 . The estimates
imply two-sided bounds for probabilities P (|Y - a| > r).


Upload: 1995

Update: 1998-04-24


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