Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering

The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameterθ:dXt=(θα(t)+β(t)Xt)dt+σ(t)dWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameterθbased on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.