, Volume 32, Issue 1, pp 47-72

Consistent parameter estimation for partially observed diffusions with small noise

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Abstract

In this paper 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.

This research was supported: by Systems Research Center, University of Maryland through NSF Grant CDR-85-00108 and AFOSR-URI Grant 87-0073; by Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, under ARO/MIT Grant DAAL-03-86-K-0171; by INRIA Sophia Antipolis, under ERO/INRIA Grant DAJA45-90-C-0008, and by the CNRS-GRAutomatique.