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Finite-dimensional stochastic filtering in discrete time: The role of convolution semigroups

  • Linear and Nonlinear Filtering
  • Conference paper
  • First Online:
Analysis and Optimization of Systes

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 144))

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Abstract

We consider a stochastic dynamic system in discrete time with an observable component Xn ∈X⊂R v (signal). The signal is a Markov chain and, at any step, the conditional density of the observation given the signal is fixed in the exponential class. We face the problem of finding transition kernels for Xn for which the system admits filters of dimension v; we reduce this problem to an analytical procedure in which the first step can be solved in terms of convolution semigroups of probability distributions.

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Authors and Affiliations

  1. Dept. of Mathematics, University “La Sapienza”, Piazzale A. Moro, 5-00185, Rome

    Fabio Spizzichino

Authors
  1. Fabio Spizzichino
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Editor information

A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Spizzichino, F. (1990). Finite-dimensional stochastic filtering in discrete time: The role of convolution semigroups. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120046

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  • DOI: https://doi.org/10.1007/BFb0120046

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52630-8

  • Online ISBN: 978-3-540-47085-4

  • eBook Packages: Springer Book Archive

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