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...

The geometric Brownian motion is the solution of a linear stochastic differential equation in the Itô-sense. If one adds to the drift term a possible nonlinear time delayed term and starts with a nonnegative initial process then the process generated in this way, may hit zero and may oscillate...

Assume L is a non-deterministic real valued Lévy process and f is a smooth function on [0,t]

We obtain an explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and get explicit rates of decrease for error probabilities of Neyman-Pearson, Bayes, and minimax tests. We also give expressions for the rates of...