Estimation for Some Classes of Gaussian Markov Processes

In the paper we consider a class of Gaussian Markov processes y(t). For e fixed t ∈[O,T],the random vector y(t) may be interpreted as a vector of observations in a classical linear model. We give a minimal sufficient statistic and obtain a simple characterization of its completeness. Using the terminology of stochastic integrals we give explicit formulas for estimators of regression coefficients and variance components. Moreover, we prove that they are the best unbiased estimators. Such problems are considered in detection, modulation, communication and control. We use here the same notation and terminology as in [7].