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1995-07

On Distribution of Quadratic Forms in Gaussian Random Variables

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


Series: 1995-07, Preprints

MSC:
60B11 Probability theory on linear topological spaces
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).

Keywords:

This paper was published in:
Teor. Veroyatn. Primen. 40 (1995),