, Volume 20, Issue 2, pp 389–411 | Cite as

Multiplicative Kalman filtering

  • Fabienne Comte
  • Valentine Genon-Catalot
  • Mathieu Kessler
Original Paper


We study a non-linear Hidden Markov Model, where the process of interest is the absolute value of a discretely observed Ornstein–Uhlenbeck diffusion, which is observed after a multiplicative perturbation. We obtain explicit formulae for the recursive relations which link the relevant conditional distributions. As a consequence the predicted, filtered, and smoothed distributions for the hidden process can easily be computed. We illustrate the behaviour of these distributions on simulations.


Filtering Discrete time observations Hidden Markov Models Parametric inference Scale perturbation 

Mathematics Subject Classification (2000)

60G35 62M05 60J60 


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2010

Authors and Affiliations

  • Fabienne Comte
    • 1
  • Valentine Genon-Catalot
    • 1
  • Mathieu Kessler
    • 2
  1. 1.Laboratoire MAP 5Université Paris Descartes, UFR de Mathématiques et Informatique, CNRS UMR 8145Paris Cedex 06France
  2. 2.Departamento de Matemática Aplicada y EstadísticaUniversidad Politécnica de CartagenaCartagenaSpain

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