Statistic analysis of stochastic resonance with ergodic diffusion noise

A subthreshold signal is transmitted through a channel and may be detected when some noise { with known structure and proportional to some level { is added to the data. There is an optimal noise level, called stochastic resonance, that corresponds to the highest Fisher information in the problem of estimation of the signal. As noise we consider an ergodic difusion process and the asymptotic is considered as time goes to infnity. We propose consistent estimators of the subthreshold signal and we solve further a problem of hypotheses testing. We also discussevidence of stochastic resonance for both estimation and hypotheses testing problems via examples.