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Zbl 1085.62106
Deck, T.
Asymptotic properties of Bayes estimators for Gaussian Itô\,-\,processes with noisy observations. (English)
[J] J. Multivariate Anal. 97, No. 2, 563-573 (2006). ISSN 0047-259X

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 2000:: *62M20 Prediction, etc. (statistics)
62F15 Bayesian inference
62F12 Asymptotic properties of parametric estimators
60H10 Stochastic ordinary differential equations
62M05 Markov processes: estimation

Keywords: linear filtering

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Zentralblatt MATH Berlin [Germany]