A functional form for a particular coefficient of ergodicity

Abstract

Seneta, in a recent paper, presented a general treatment of the concept of ‘coefficient of ergodicity', τ (P), for a finite stochastic matrix P. In this paper, a functional form for τ ∞(P) in terms of the attributes of P is determined. It is shown that, by increasing the dimension of P, τ ∞(Ρ) can assume any large value. In view of this, τ ∞ will be practically useful only in the case τ ∞(P) ≦ τ 1(P), where τ 1(P) is the well-known Dobrushin or delta coefficient.