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),