Estimating unobservable signal by Markovian noise induction. When noise helps in Statistics!

A sub threshold 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 of stochastic resonance, that corresponds to the minimum variance of the estimators in the problem of recovering unobservable signals. 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 sub threshold signal and we solve further a problem of hypotheses testing. We also discuss evidence of stochastic resonance for both estimation and hypotheses testing problems via examples.