On parameter estimation of the hidden Gaussian process in perturbed SDE.

Abstract

We present results on parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as the MLE, but much more simple to calculate, the estimators are so-called “estimator-processes”. The construction of the estimators is based on the equations of Kalman-Bucy filtration and the asymptotic corresponds to the small noises in the observations and state (hidden process) equations. We give conditions which provide the consistency, asymptotic normality and asymptotic efficiency of the proposed estimators.