Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We consider two models of Markov processes observed (continuous time) in white Gaussian noise. One is telegraph signal with two states (ergodic case) and the second is partially observed linear system with small noise in observation equation. For both models we construct the MLE and One-step MLEs of the unknown parameters and show the consistency, asymptotic normality, convergence of moments and the asymptotic minimax efficiency of these estimators.