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,.).
Iterate Logarithm Conditional Probability Distribution Random System Stationary Increment Functional Central Limit Theorem
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