Consider a Markoff chain (by which is meant a stochastic process defined for discrete values of both variable and parameter, and whose probability dependence does not extend to more than a unit interval) with completely specified transition probability matrix P = (pij), where pij is the conditional probability that the (r + 1)th observation belongs to the state Ei, given that the rth observation belongs to the state Ei for r≥ I. We assume that there are a states E1, E2, …, Ea, where a is finite. We also assume an ergodic property for the stochastic process, that is, we consider non-periodic chains for which all the possible initial states remain permanently available. This defines what has been called the positively regular case. Also under the above assumption the moduli of all the latent roots λr of the transition probability matrix P = (pij) other than the first simple latent root λ1 = 1 are less than one (see Bartlett(1)).