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On The Spectral Properties Of A Markov Model For Learning Processes

Author

Listed:
  • I. ANTONIOU

    (International Solvay Institutes for Physics and Chemistry C.P.231, Boulevard du Triomphe, 1050 Brussels, Belgium;
    Theoretische Naturkunde, Free University of Brussels, Belgium)

  • F. BOSCO

    (International Solvay Institutes for Physics and Chemistry C.P.231, Boulevard du Triomphe, 1050 Brussels, Belgium;
    Departamento de Fisica, Universidade Federal do Espirito Santo, 29060-900 Vitoria ES, Brazil)

Abstract

We study the spectral properties of the evolution operator of densities of the one-dimensional version of a Markov model for instrumental conditioning proposed by Bush and Mosteller in the early '50s. The model is a probabilistic combination of dynamical systems with phase space dependent probability distribution. The spectral properties are derived by restricting the stochastic operator in the space of analytic functions. The nonergodic properties of the model are demonstrated by the spectrum of the stochastic operator.

Suggested Citation

  • I. Antoniou & F. Bosco, 2000. "On The Spectral Properties Of A Markov Model For Learning Processes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 213-220.
    • Handle: RePEc:wsi:ijmpcx:v:11:y:2000:i:02:n:s0129183100000201
    DOI: 10.1142/S0129183100000201
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