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Martin boundaries of cartesian products of markov chains

Published online by Cambridge University Press:  22 January 2016

Massimo A. Picardello  and
Wolfgang Woess
Massimo A. Picardello
Affiliation:
Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, 00133 Roma, Italy
Wolfgang Woess
Affiliation:
Dipartimento di Matematica, Universitá di Milano, 20133 Milano, Italy
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Let P and Q be the stochastic transition operators of two time-homogeneous, irreducible Markov chains with countable, discrete state spaces X and Y, respectively. On the Cartesian product Z = X x Y, define a transition operator of the form Ra = a·P + (1 — a) · Q, 0 < a < 1, where P is considered to act on the first variable and Q on the second. The principal purpose of this paper is to describe the minimal Martin boundary of Ra (consisting of the minimal positive eigenfunctions of Ra with respect to some eigenvalue t, also called t-harmonic functions) in terms of the minimal Martin boundaries of P and Q.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 128 , December 1992 , pp. 153 - 169
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

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