On Detection of Gaussian Stochastic Sequences

Abstract

We consider the minimax detection problem for a Gaussian random signal vector in white Gaussian additive noise. It is assumed that an unknown vector σ of signal vector intensities belongs to a given set ε. We investigate when it is possible to replace the set ε with a smaller set ε₀ without loss of quality (and, in particular, replace it with a single point σ₀).