# Asymptotic Properties of Learning Models

## 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 S_{n} (an indicator of the subject’s response tendencies) at the beginning of the trial. S_{n} is a random variable taking on values in a measurable state space (S,S). On trial n an event E_{n} _{+1} occurs that results in a change of state. E_{n} _{+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, E_{n} _{+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 S_{n} _{+1} = v(S_{n}, E_{n} _{+1}), n ≥ 0. Finally, we assume that the conditional probability distribution of E_{n} _{+1} given E_{n}, S_{n},... depends only on the state S_{n} and denote it Q(S_{n},.).

### Keywords

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