Estimating unobservable signal by Markovian noise induction

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 unobservable signal. For several noise structures it has been shown the evidence of stochastic resonance effect. Here we study the case when the noise is a Markovian process. We propose consistent estimators of the subthreshold signal and we solve further a problem of hypotheses test- ing. We also discuss evidence of stochastic resonance for both estimation and hypotheses testing problems via examples.