Applied Mathematics and Optimization

, Volume 32, Issue 1, pp 47–72

Consistent parameter estimation for partially observed diffusions with small noise

  • M. R. James
  • F. Le Gland

DOI: 10.1007/BF01189903

Cite this article as:
James, M.R. & Le Gland, F. Appl Math Optim (1995) 32: 47. doi:10.1007/BF01189903


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 estimationNonlinear filteringLarge deviations

AMS classification


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