Nonparametric estimation problem for a time-periodic signal in a periodic noise

In this paper we construct a kernel estimator of a periodic signal when the observation follows the model dζt=f(t)dt+σ(t)dWt, where f,σ:R→R are continuous periodic and {Wt,t≥0} is a Brownian motion. We state its consistency as well as the asymptotic normality.