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Consistent parameter estimation for partially observed diffusions with small noise

Matthew R. James 1 François Le Gland 2
2 AS - Signal Processing and Control
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
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.
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https://hal.inria.fr/hal-00912056
Contributor : Francois Le Gland <>
Submitted on : Monday, December 2, 2013 - 1:14:06 AM
Last modification on : Tuesday, June 15, 2021 - 4:21:54 PM

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Matthew R. James, François Le Gland. Consistent parameter estimation for partially observed diffusions with small noise. Applied Mathematics and Optimization, Springer Verlag (Germany), 1995, 32 (1), pp.47-72. ⟨10.1007/BF01189903⟩. ⟨hal-00912056⟩

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