On the stability of signal detection

One of the basic problems in statistical communication theory is that of detecting, at the end of a communication channel, a signal imbedded in noise. The Gaussian model is a model for which the noise as well as the received signal are Gaussian processes with equivalent laws, so that the resulting detection problem is nonsingular. Unfortunately most solutions to problems involving signals in Gaussian noise are based on a knowledge of the auto-correction function or spectrum (if the noise is stationary). This document studies the probabilties of false alarm and false dismissal for sure signals embedded in additive noise. The noise is contaminated Gaussian, and the framework is such that continuous-time problems can be studied.