Receiver operating characteristic curves for a simple stochastic process that carries a static signal.

摘要: The detection of a weak signal in the presence noise is an important problem that often studied terms receiver operating characteristic (ROC) curve, which probability correct plotted against for false positive. This kind analysis typically applied to situation and are stochastic variables; emerges, however, also context both processes (correct or false) said take place when process crosses threshold given time window. Here we consider combination static has be detected dynamic process, well-known Ornstein-Uhlenbeck process. We give exact (but difficult evaluate) quadrature expressions rates positives detections, investigate systematically simple sampling approximation suggested earlier, compare by Stratonovich limit high threshold, briefly explore case multiplicative signal; all theoretical results compared extensive numerical simulations corresponding Langevin equation. Our demonstrate provides reasonable description ROC curve this system, it clarifies cases curve.