Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations

The estimation of a real parameter [theta] in a linear stochastic differential equation of the simple type is investigated, based on noisy, time continuous observations of Xt. Sufficient conditions on the continuous functions [beta] and [sigma] are given such that the (conditionally normal) Bayes estimators of [theta] satisfy certain error bounds and are strongly consistent.