Hypothesis testing for signal detection problem and large deviations

Abstract

We consider a signal detection problem for the continuous-time stationary diffusion processes. The optimal decision region is given by Neyman-Pearson's lemma. We establish certain large deviation estimates, and with the help of it we show that the error probability of the second kind of the signal detection tends to zero or one exponentially fast, depending on the fixed exponent of the decay of the error probability of the first kind, as the observation time goes to infinity.