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Asymptotic Properties of Learning Models

  • Marius Iosifescu
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 20)

Abstract

It is already well known that all stochastic models for learning studied up to now enter the following general scheme (cf.Norman (1972)). The behaviour of the subject on trial n = 0,1,... is determined by his state Sn (an indicator of the subject’s response tendencies) at the beginning of the trial. Sn is a random variable taking on values in a measurable state space (S,S). On trial n an event En +1 occurs that results in a change of state. En +1 is a randon variable taking on values in a measurable event space (E,E) and specifies those occurrences on trial n that affect subsequent behaviour. Typically, En +1. includes a specification of the subject’s response and its observable outcome or payoff. To represent the fact that the occurrence of an event effects a change of state we consider a measurable mapping v of S × E into S and postulate that Sn +1 = v(Sn, En +1), n ≥ 0. Finally, we assume that the conditional probability distribution of En +1 given En, Sn,... depends only on the state Sn and denote it Q(Sn,.).

Keywords

Iterate Logarithm Conditional Probability Distribution Random System Stationary Increment Functional Central Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Marius Iosifescu
    • 1
  1. 1.Centre of Mathematical StatisticsBucharestRomania

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