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

MSC:

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

Citations:

Zbl 0129.107
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References:

[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
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