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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
linear filtering
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