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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.

62M20Prediction; filtering (statistics)
62F15Bayesian inference
62F12Asymptotic properties of parametric estimators
60H10Stochastic ordinary differential equations
62M05Markov processes: estimation
Full Text: DOI
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