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.
