Computation of the stationary distribution of an infinite Markov matrix

Abstract

An algorithm is presented for computing the unique stationary distribution of an infinite stochastic matrix possessing at least one column whose elements are bounded away from zero.Elementwise convergence rate is discussed by means of two examples.

Non-negative Matrices and Markov Chains

“…The argument of the remainder of §7.1, and of §7.2 is condensed and synthesized from Golub and Seneta (1974), Allen, Anderssen and Seneta (1977), and Seneta (1980). Related papers are Golub and Seneta (1973) and Paige, Styan and Wachter (1975). The reader interested in practical situations where such approximative procedures from finite truncations are necessary should consult Beckmann, McGuire and Winsten (1956) and Bithell (1971).…”

“…(Lopez, 1961;Seneta, 1973) 3.11. If all H b k 2 1, have the same incidence matrix which is irreducible and has at least one positive diagonal entry, show that H p,, > 0 for p 2 0, r 2 2(n -1 ).…”

“…Treatments within monographs are given by Bernstein (1946,1964), Paz (1971), Seneta (1973), Isaacson and Madsen (1976) and Iosifescu (1977); these provide references additional to those listed in this book.…”

Bounded truncation error for long-run averages in infinite Markov chains

“…While corresponding truncation approximations of stationary distributions have been studied quite extensively, see [9], [11], [13], [14], [16], [24], [25], and [18,Chapter 7], there is a lack of similar studies for ψf or its special case of stationary expectations. for computational purposes.…”

Recent Advances in Iterative Methods

“…Golub and Senata ('73) [62] proved monotonic convergence of an algorithm for finding the stationary vector of an infinite Markov chain. They made use of a sequence of finite approximations from upper left hand truncations of the matrix.…”