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Consistent parameter estimation for partially observed diffusions with small noise. (English) Zbl 0822.62068
Summary: We provide a consistency result for the MLE for partially observed diffusion processes with small noise intensities. We prove that if the underlying deterministic system enjoys an identifiability property, then any MLE is close to the true parameter if the noise intensities are small enough. The proof uses large deviations limits obtained by PDE vanishing viscosity methods. A deterministic method of parameter estimation is formulated. We also specialize our results to a binary detection problem, and compare deterministic and stochastic notions of identifiability.

MSC:
62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
93E11 Filtering in stochastic control theory
93E10 Estimation and detection in stochastic control theory
60F10 Large deviations
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