On frequency estimation for a periodic ergodic diffusion process

We consider the problem of frequency estimation by observations for a periodic diffusion process possessing ergodic properties in two different situations. The first corresponds to a trend coefficient continuously differentiable with respect to parameter, and the second, to a 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 rate $T^2$.