An extension of cusp estimation problem in ergodic diffusion processes

We consider a non-regular estimation problem in ergodic diffusion processes whose drift coefficient includes a component x-[theta]p with . This is an extension of the work of Dachian and Kutoyants (2003) that deals with the case . We study the asymptotic behavior of the Bayes estimator via Ibragimov and Khasminskii's approach. Its convergence rate and asymptotic distribution are given. Furthermore, the Bayes estimator is asymptotically efficient in a certain minimax sense.