Distribution of the fractional parts of random vectors: The Gaussian case. I. (English. Russian original) Zbl 1059.60016

Kulikova, A. A.; Prokhorov, Yu. V.

Theory Probab. Appl. 48, No. 2, 355-359 (2003); translation from Teor. Veroyatn. Primen. 48, No. 2, 399-402 (2003).

A fractional distribution of an \(s\)-dimensional Gaussian random vector is considered. A deviation of this distribution from the uniform one on \(s\)-dimensional unit cube is estimated by functions of the minimal and maximal eigenvalues of the covariance matrix. The main attention of this part of the paper is devoted to the case of small values of \(s\).

Reviewer: Jaroslaw Bartoszewicz (Wrocław)

MSC:

60E05

Probability distributions: general theory

Keywords:

uniform distribution; Poisson summation formula; fractional Gaussian vectors