A central limit theorem for processes defined on a finite Markov chain

Abstract

We shall be concerned in this paper with a class of temporally homogeneous Markov processes, {R(t), X(t)}, in discrete or continuous time taking values in the spaceThe marginal process {X(t)} in discrete time is, in the terminology of Miller (10), a sequence of random variables defined on a finite Markov chain. Probability measures associated with these processes are vectors of the formwhereWe shall call a vector of the form of (0·2) a vector distribution.