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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 \(\theta\) in a linear stochastic differential equation of the simple type \(dX_t=\theta\beta(t)dt + \sigma(t)dB_t\) is investigated, based on noisy, time continuous observations of \(X_t\). 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.

MSC:
62M20 Inference from stochastic processes and prediction
62F15 Bayesian inference
62F12 Asymptotic properties of parametric estimators
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62M05 Markov processes: estimation; hidden Markov models
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