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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.

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
Full Text: DOI
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