A LIMIT THEOREM OF A FUNCTIONAL OF REGULAR MARKOV PROCESSES AND ITS APPLICATIONS TO LEARNING MODELS

We introduce a new interpretation of a phenomenon followed by certain subsequent learning experiments such as shift problems in discrimination learning, and show some limit theorems representing the rightness of such experiments on the basis of our interpretation. In this paper we treat a regular Markov chain {X,,}7,>0 as a mathematical model for subjects' behavior in the first phase and a family of stopping times {Ng (d) } d>o for selecting the time when we change the first phase into the second phase, and show that the asymptotic distribution of { f (XNg (d)) } d>o is the same as the asym ptotic distribution of If (Xn) } n5o under some conditions.