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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:
62M20Prediction; filtering (statistics)
62F15Bayesian inference
62F12Asymptotic properties of parametric estimators
60H10Stochastic ordinary differential equations
62M05Markov processes: estimation
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References:
[1] Arató, M.: Linear stochastic systems with constant coefficients. Lecture notes in control and information sciences 45 (1982) · Zbl 0544.93060
[2] Basawa, I. V.; Rao, B. L. S. Prakasa: Statistical inference for stochastic processes. (1980) · Zbl 0448.62070
[3] Davis, M. H. A.: Linear estimation and stochastic control. (1977) · Zbl 0437.60001
[4] Deck, T.; Theting, T.: Robust parameter estimation for stochastic differential equations. Acta appl. Math. 84, 279-314 (2004) · Zbl 1062.62156
[5] J.L. Doob, Applications of the theory of martingales, Colloque Internat. CNRS, 1949, 22 -- 28. · Zbl 0041.45101
[6] Kallianpur, G.; Selukar, R. S.: Parameter estimation in linear filtering. J. multivariate anal. 39, No. 2, 284-304 (1991) · Zbl 0768.62086
[7] Krishnaprasad, P. S.; Marcus, S.; Hazewinkel, M.: Current algebras and the identification problem. Stochastics 11, No. 1 -- 2, 65-101 (1983) · Zbl 0541.93070
[8] Kunita, H.: Asymptotic behavior of the nonlinear filtering errors of Markov processes. J. multivariate anal. 1, 365-393 (1971) · Zbl 0245.93027
[9] Yu A. Kutoyants, Parameter Estimation for Stochastic Processes, Heldermann Verlag, Berlin, 1984. · Zbl 0542.62073
[10] Lipster, R. S.; Shiryayev, N.: Statistics of random processes I and II. (2001)
[11] A. O’Hagan, Bayesian Inference, Kendalls Advanced Theory of Statistics, vol. 2B, Arnold, New York, 1999.
[12] øksendal, B.: Stochastic differential equations. (1998) · Zbl 0897.60056
[13] B.L.S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Kendall’s Library of Statistics, vol. 8, Arnold, London, 1999.
[14] Schwartz, L.: On Bayes procedures. Z. wahrsch. Theo. 4, 10-26 (1965) · Zbl 0158.17606
[15] Walter, W.: Gewöhnliche differentialgleichungen. (1972) · Zbl 0247.34001