On detection of Gaussian stochastic sequences

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particular, to replace it by a single point $\boldsymbol{\sigma}_{0}$).Comment: Problems of Information Transmission, vol. 53, no. 4, pp. 47--66, 201

Two theorems on distribution of Gaussian quadratic forms

New results on comparison of distributions of Gaussian quadratic forms are presentedComment: Problems of Information Transmission, v. 53, no. 3, pp. 3--15, 201