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...

We consider the problem of [theta]-parameter estimation by observations of the linear process dXt=[theta]Xt dt+[var epsilon]dWt, XO=xO, O[less-than-or-equals, slant]t[less-than-or-equals, slant]T, where [var epsilon] is a "small" parameter. The asymptotics ([var epsilon] -- 0) of minimum L1-norm...

We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposed that under the basic hypothesis the trend coefficient depends on a finite-dimensional parameter and we study the Cramér-von Mises type...

Large sample statistical analysis of threshold autoregressive models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric correlation tail and derive a complete characterization of the...

We consider two problems of constructing of goodness of fit tests for ergodic diffusion processes. The first one is concerned with a composite basic hypothesis for a parametric class of diffusion processes, which includes the Ornstein–Uhlenbeck and simple switching processes. In this case we...