Applied Mathematics and Optimization

, Volume 32, Issue 1, pp 47–72 | Cite as

Consistent parameter estimation for partially observed diffusions with small noise

  • M. R. James
  • F. Le Gland
Article

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.

Key words

Parameter estimation Nonlinear filtering Large deviations 

AMS classification

62F12 93E10 93E11 60F10 

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Copyright information

© Springer-Verlag New York Inc 1995

Authors and Affiliations

  • M. R. James
    • 1
  • F. Le Gland
    • 2
  1. 1.Department of Systems EngineeringAustralian National UniversityCanberraAustralia
  2. 2.Institut de Recherche en Informatique et Systèmes Aléatoires, Institut National de Recherche en Informatique et en AutomatiqueRennes CédexFrance

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