Chains of infinite order and their application to learning theory

Introduction* The purpose of this paper is to study the asymptotic behavior of a large class of stochastic processes which have been used as models of learning experiments. We will do this by applying a theory of so-called "chains of infinite order" or "chanes a liaisons completes." Namely, we shall employ certain limit theorems for stochastic processes whose transition probabilities depend on the entire past history of the process, but only slightly on the remote past. Such theorems were given by Doeblin and Fortet [3] in a form close to that we employ; however, in order to accomodate certain cases of learning models we found it necessary to relax somewhat their hypotheses. A self-contained discussion of these and some additional results is the content of 2.