**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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