On frequency estimation of periodic ergodic diffusion process

Abstract

We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter trend coefficient and the second - to discontinuous trend coefficient. It is shown that in the first case the maximum likelihood and bayesian estimators are asymptotically normal with rate $T^{3/2}$ and in the second case these estimators have different limit distributions with the rate $T^2$.