We consider adaptive Bayesian estimation of both drift and diffusion coefficient parameters for ergodic multidimensional diffusion processes based on sampled data. Under a general condition on the discretization step of the sampled data, three kinds of adaptive Bayes type estimators are proposed...

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$ is observed only when its path lies over some threshold $\tau$. On the basis of the observable part of the trajectory, the problem is to estimate finite dimensional parameter in both drift and diffusion coefficient under a discrete...

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$ is observed only when its path lies over some threshold $\tau$. On the basis of the observable part of the trajectory, the problem is to estimate finite dimensional parameter in both drift and diffusion coefficient under a discrete...

For a one-dimensional diffusion process , we suppose that X(t) is hidden if it is below some fixed and known threshold [tau], but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is the estimation of a finite-dimensional parameter in...

We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes crucial to prove nondegeneracy of a key index χ0. By...

We consider the model selection problem for ergodic diffusion processes based on sampled data. The adaptive estimators for parameters of drift and diffusion coefficients are used in order to construct Akaike’s information criterion (AIC) type model selection statistics. Asymptotic properties...