ON THE SPECTRAL PROPERTIES OF A MARKOV MODEL FOR LEARNING PROCESSES

I. Antoniou () and F. Bosco ()
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I. Antoniou: International Solvay Institutes for Physics and Chemistry C.P.231, Boulevard du Triomphe, 1050 Brussels, Belgium;
F. Bosco: International Solvay Institutes for Physics and Chemistry C.P.231, Boulevard du Triomphe, 1050 Brussels, Belgium;

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 02, 213-220

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.

Keywords: Learning Processes; Markov Processes; Discrete Dynamics; Spectral Decomposition; Statistical Description of Chaos (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0129183100000201

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