Hypothesis testing for signal detection problem and large deviations

We consider a signal detection problem for the continuous-time stationary d iffusion 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 d etection tends to zero or one exponentially fast, depending on the fixed ex ponent of the decay of the error probability of the first kind, as the obse rvation time goes to infinity.