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Asymptotic properties of a certain class of Bush–Mosteller learning models

Published online by Cambridge University Press:  01 July 2016

Peter Findeisen
Peter Findeisen*
Affiliation:
University of Düsseldorf
*
∗Postal address: Psychologisches Institut der Universität Düsseldorf, Lehrstuhl für Psychologie IV, 4000 Düsseldorf, Universitätsstrasse 1, W. Germany.
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Abstract

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.

Keywords

RANDOM SYSTEMS WITH COMPLETE CONNECTIONSLEARNING MODELSBUSH–MOSTELLER MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 922 - 941
Copyright
Copyright © Applied Probability Trust 1980 

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References

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