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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 Prediction; filtering (statistics) 62F15 Bayesian inference 62F12 Asymptotic properties of parametric estimators 60H10 Stochastic ordinary differential equations 62M05 Markov processes: estimation
linear filtering
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##### References:
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