In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent...

For i.i.d. Poisson point processes with intensity measure [Lambda] an estimator for [theta][infinity]([Lambda]) = [integral operator] [infinity] d[Lambda] is introduced. Consistency as well as rates for the convergence are established. An Edgeworth-type expansion for the distribution function is...

A problem of hypothesis testing is considered for a model of diffusion process with diusion coecient tending to zero. A simple hypothesis and a semiparametric alternative are formulated in the terms of the values of some functional of nonperturbed trajectory of the dynamical system. The test...

Two classes of unbiased estimators of the density function of ergodic distribution for the diffusion process of observations are proposed. The estimators are square-root consistent and asymptotically normal. This curious situation is entirely different from the case of discrete-time models...

We consider the problems of the density and distribution function estimation by the observations of diffusion process with ergodic properties. In every problem we first propose a minimax bound on the risk of any estimator and then study the asymptotic behavior of several estimators. It is shown...