Nagoya Mathematical Journal

Martin boundaries of Cartesian products of Markov chains

Massimo A. Picardello and Wolfgang Woess

Full-text: Open access

Article information

Nagoya Math. J. Volume 128 (1992), 153-169.

First available in Project Euclid: 14 June 2005

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J50: Boundary theory


Picardello, Massimo A.; Woess, Wolfgang. Martin boundaries of Cartesian products of Markov chains. Nagoya Math. J. 128 (1992), 153--169.

Export citation


  • [Do] J. L. Doob, Discrete potential theory and boundaries, J. Math. Meth., 8 (1959), 433-458.
  • [Fr] A. Freire, On the Martin boundary of Riemannian products, in J. Diff. Geom., 33 (1991), 215-232
  • [GT] Y. Guivarc'h, J. C. Taylor, The Martin compactification of the polydisc at the bot-
  • [Hu] G. A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math., 4 (1960), 313-340.
  • [Ka] V. A. Kaimanovich, The differential entropy of the boundary of a random walk on a group, Russian Math. Surveys, 38 5 (1983), 142-143.
  • [KV] V. A. Kaimanovich, A.M. Vershik, Random walks on discrete groups boundary and entropy, Ann. Prob., 11 (1983), 457-490.
  • [KSK] J. G. Kemeny, J. L. Snell, A. W. Knapp, Denumerable Markov Chains, 2nd ed., Springer, New York-Heidelberg-Berlin, 1976.
  • [Ml] S. A. Molchanov, On the Martin boundaries for the direct products of Markov chains, Theory of Prob. and Its Appl., 12 (1967), 307-314.
  • [M2] S. A. Molchanov, Martin boundaries for the direct product of Markov processes, Siberian J. Math., 11 (1970), 280-287.
  • [PS] M. A. Picardello, P. Sjgren, Boundary behaviour of eigenfunctions of the Lapla- cian in a bi-tree, J. Reine Angew. Math., 424 (1992), 137-148.
  • [PW] M. A. Picardello, W. Woess, Examples of stable Martin boundaries of Markov chains, in Potential Theory (ed. M. Kishi), de Gruyter. Berlin-New York (1991), 261-270.
  • [Pr] W. E. Pruitt, Eigenvalues of nonnegative matrices, Ann. Math. Statistics., 35 (1964), 1797-1800.
  • [Ta] J. C. Taylor, The product of minimal functions is minimal, Bull. London Math. Soc. 22 (1990), 499-504, erratum, Bull, London Math. Soc. 24 (1991), 379-380.
  • [Ve] D. Vere-Jones, Geometric ergodicity in denumerable Markov chains, Quart. J. Math. Oxford, 13(1962), 7-28. Massimo A. Picardello Dipartimento di Matematica Universit di RomaTor Vergata 00133 Roma, Italy Wolfgang Woess Dipartimento di Matematica Universit diMilano 20133 Milano, Italy