Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The minimal harmonic functions of sojourn processes of certain finite state Markov chains

Author: E. Bolthausen
Journal: Proc. Amer. Math. Soc. 77 (1979), 138-144
MSC: Primary 60J10; Secondary 60J50
MathSciNet review: 539647
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: To a finite state, discrete time Markov chain a new chain is constructed which counts the number of sojourns in each state. This sojourn process is a transient Markov chain. The minimal harmonic functions of this chain are identified.

References [Enhancements On Off] (What's this?)

  • [1] D. Blackwell and D. G. Kendall, The Martin boundary of Pólya's scheme and an application to stochastic population growth, J. Appl. Probability 1 (1964), 248-296.
  • [2] G. Choquet, Lectures on analysis, Benjamin, Reading, Massachusetts, 1969.
  • [3] J. N. Darroch and E. Seneta, On quasi-stationary distributions in absorbing discrete-time finite Markov chains, J. Appl. Probability 2 (1965), 88–100. MR 0179842
  • [4] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time. I. II, Comm. Pure Appl. Math. 28 (1975), 1–47; ibid. 28 (1975), 279–301. MR 0386024
  • [5] John G. Kemeny, J. Laurie Snell, and Anthony W. Knapp, Denumerable Markov chains, 2nd ed., Springer-Verlag, New York-Heidelberg-Berlin, 1976. With a chapter on Markov random fields, by David Griffeath; Graduate Texts in Mathematics, No. 40. MR 0407981
  • [6] J. Lamperti and J. L. Snell, Martin boundaries for certain Markov chains, J. Math. Soc. Japan 15 (1963), 113–128. MR 0152016
  • [7] D. Revuz, Markov chains, 2nd ed., North-Holland Mathematical Library, vol. 11, North-Holland Publishing Co., Amsterdam, 1984. MR 758799

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60J10, 60J50

Retrieve articles in all journals with MSC: 60J10, 60J50

Additional Information

Keywords: Markov chain, sojourn times, harmonic functions, Martin boundary
Article copyright: © Copyright 1979 American Mathematical Society