Solidarity properties and a Doeblin decomposition for a class of non-Markovian stochastic processes

Abstract

We are concerned with solidarity and a Doeblin decomposition for a class of non-Markovian discrete parameter stochastic processes. Since any such process is associated with a certain general Markov chain whose transition probability function has a special form, we use the theory of Markov chains with continuous components to this particular chain in order to get properties of the non-Markovian process. We illustrate our results on a model closely related to learning theory.