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Asymptotic properties of Bayes estimators for Gaussian Itô - processes with noisy observations. (English) Zbl 1085.62106
Summary: The estimation of a real parameter θ in a linear stochastic differential equation of the simple type dX t =θβ(t)dt+σ(t)dB t is investigated, based on noisy, time continuous observations of X t . Sufficient conditions on the continuous functions β and σ are given such that the (conditionally normal) Bayes estimators of θ satisfy certain error bounds and are strongly consistent.
MSC:
62M20Prediction; filtering (statistics)
62F15Bayesian inference
62F12Asymptotic properties of parametric estimators
60H10Stochastic ordinary differential equations
62M05Markov processes: estimation