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Large deviations inequalities for the maximum likelihood estimator and the Bayes estimators in nonlinear stochastic differential equations. (English) Zbl 0936.60024

Exponential bounds of large deviations are established for the maximum likelihood as well as for the Bayes estimator of a one-dimensional drift parameter of diffusion processes. The proof employes a general approach of Ibragimov and Khasminskij for getting exponential bounds for the maximum likelihood estimator for any sequence of experiments.
Reviewer: F.Liese (Rostock)

MSC:

60F10 Large deviations
62F12 Asymptotic properties of parametric estimators
62M05 Markov processes: estimation; hidden Markov models
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