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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