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Iterated function systems a rising from recursive estimation problems
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  • Published: March 1992

Iterated function systems a rising from recursive estimation problems

  • J. H. Elton1 &
  • M. Piccioni2 

Probability Theory and Related Fields volume 91, pages 103–114 (1992)Cite this article

  • 98 Accesses

  • 18 Citations

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Summary

We show that under suitable conditions the one-step predictor of a finite-state Markov chain from noisy observations has a unique stationary law which is supported by a self-similar set, called the attractor. Under additional symmetry conditions such attractor is either connected, or totally disconnected and perfect. In this latter case the predictor keeps an infinite memory of the past observations. The main problem of interest is to identify those values of the parameters of the chain and the observation process for which this happens. In the binary case, the problem is completely solved. In higher dimension the problem is harder: a complete solution is presented for ternary chains in the completely symmetric persistent case.

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Authors and Affiliations

  1. Georgia Institute of Technology and Iterated Systems, Atlanta, USA

    J. H. Elton

  2. Dipartimento di Matematica Università di L'Aquila and Centro V. Volterra, Università di Roma Tor Vergata, 1-00173, Roma, Italy

    M. Piccioni

Authors
  1. J. H. Elton
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  2. M. Piccioni
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Cite this article

Elton, J.H., Piccioni, M. Iterated function systems a rising from recursive estimation problems. Probab. Th. Rel. Fields 91, 103–114 (1992). https://doi.org/10.1007/BF01194492

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  • Received: 31 May 1990

  • Revised: 20 July 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01194492

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Keywords

  • Markov Chain
  • Function System
  • Mathematical Biology
  • Estimation Problem
  • Suitable Condition
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