The minimal harmonic functions of sojourn processes of certain finite state Markov chains. (English) Zbl 0416.60077


60J05 Discrete-time Markov processes on general state spaces
60J45 Probabilistic potential theory
60J50 Boundary theory for Markov processes


Zbl 0129.107
Full Text: DOI


[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. · Zbl 0129.10702
[2] G. Choquet, Lectures on analysis, Benjamin, Reading, Massachusetts, 1969. · Zbl 0181.39602
[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. · Zbl 0134.34704
[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. · Zbl 0323.60069
[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. · Zbl 0348.60090
[6] J. Lamperti and J. L. Snell, Martin boundaries for certain Markov chains, J. Math. Soc. Japan 15 (1963), 113 – 128. · Zbl 0133.10504
[7] D. Revuz, Markov chains, 2nd ed., North-Holland Mathematical Library, vol. 11, North-Holland Publishing Co., Amsterdam, 1984. · Zbl 0539.60073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.