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

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 space The 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 form where We shall call a vector of the form of (0·2) a vector distribution .