On Hypothesis Discrimination under Limited Observation Resources and Limited Information

The article considers the problem of (statistically) optimal signal detection in random noise by using polynomial functionals. It is shown that the problem can be reduced to a system of equations that utilizes complete information on the random functions under consideration. This system is investigated under certain conditions; in particular, a linearized system corresponding to small signals is obtained, this being now determined only by a finite array of moments of the random functions in question.