Bernoulli

  • Bernoulli
  • Volume 7, Number 2 (2001), 211-221.

Sufficient conditions for finite dimensionality of filters in discrete time: a Laplace transform-based approach

Wolfgang J. Runggaldier and Fabio Spizzichino

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Abstract

The discrete-time filtering problem can be seen as a dynamic generalization of the classical Bayesian inference problem. For practical applications it is important to identify filtering models that, analogously to the linear Gaussian model (Kalman filter), admit a finite-dimensional filter or, equivalently, a finite-dimensional family of filter-conjugate distributions. Our main purpose here is to give sufficient conditions for the existence of finite-dimensional filters. We use a method, based on the Laplace transform, which is also constructive.

Article information

Source
Bernoulli, Volume 7, Number 2 (2001), 211-221.

Dates
First available in Project Euclid: 25 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1080222084

Mathematical Reviews number (MathSciNet)
MR1828503

Zentralblatt MATH identifier
0981.62077

Keywords
dynamic Bayes formula exponential families finite-dimensional filters infinitely divisible distributions inverse Laplace transform state-space models

Citation

Runggaldier, Wolfgang J.; Spizzichino, Fabio. Sufficient conditions for finite dimensionality of filters in discrete time: a Laplace transform-based approach. Bernoulli 7 (2001), no. 2, 211--221. https://projecteuclid.org/euclid.bj/1080222084


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