Bernoulli

  • Bernoulli
  • Volume 10, Number 4 (2004), 701-720.

Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter

Valentine Genon-Catalot and Mathieu Kessler

Full-text: Open access

Abstract

We study the properties of a nonlinear model of filtering in discrete time which leads to explicit computations. The signal is a standard AR(1) process, but noises are multiplicative and non-Gaussian. If the initial distribution of the AR(1) process is taken to belong to a specified class, the prediction and optimal filters also belong to this class and the prediction and updating steps are explicit. We prove the existence of a stationary version for the prediction filter and complete the theoretical study with simulations to illustrate the behaviour of the filter.

Article information

Source
Bernoulli, Volume 10, Number 4 (2004), 701-720.

Dates
First available in Project Euclid: 23 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1093265637

Digital Object Identifier
doi:10.3150/bj/1093265637

Mathematical Reviews number (MathSciNet)
MR2076070

Zentralblatt MATH identifier
1055.62102

Keywords
discrete time observations filtering hidden Markov models multiplicative noise stability of the filtering algorithm

Citation

Genon-Catalot, Valentine; Kessler, Mathieu. Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter. Bernoulli 10 (2004), no. 4, 701--720. doi:10.3150/bj/1093265637. https://projecteuclid.org/euclid.bj/1093265637


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References

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