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On the boundary theory for Markov chains. (English) Zbl 0292.60121


MSC:

60J50 Boundary theory for Markov processes
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References:

[1] Chung, K. L., Markov Chains with Stationary Transition Probabilities (1960), Berlin Göttingen, Heidelberg: Springer, Berlin Göttingen, Heidelberg · Zbl 0092.34304
[2] Chung, K. L., On last exit times, Illinois J. Math., 4, 629-39 (1960) · Zbl 0094.32102
[3] Chung, K. L., Probabilistic Methods in Markov Chains, 35-56 (1961), Berkeley and Los Angeles: University of California Press, Berkeley and Los Angeles
[4] Chung, K. L., On the Martin boundary for Markov chains, Proc. Nat. Acad. Sci., 48, 963-968 (1962) · Zbl 0228.60030
[5] Doob, J. L., Discrete potential theory and boundaries, J. Math. Mech., 8, 433-458 (1959) · Zbl 0101.11503
[6] Feller, W., Boundaries induced by positive matrices, Trans. Amer. Math. Soc., 83, 19-54 (1956) · Zbl 0071.34901
[7] Feller, W., On boundaries and lateral conditions for the Kolmogorov differential equations, Ann. of Math., 65, 527-570 (1957) · Zbl 0084.35503
[8] Hunt, G. A., Markoff chains and Martin boundaries, Illinois J. Math., 4, 313-340 (1960) · Zbl 0094.32103
[9] Lévy, P., Systèmes markoviens et stationnaires; cas dénombrable, Ann. École Norm., 68, 3, 327-381 (1951) · Zbl 0044.33803
[10] Neveu, J., Une généralisation des processus à accroisements croissants indépendants, Abh. Math. Mem. Univ. Hamburg, 25, 36-61 (1961) · Zbl 0103.36303
[11] Neveu, J., Lattice methods and submarkovian processes, 347-391 (1961), Berkeley and Los Angeles: University of California Press, Berkeley and Los Angeles · Zbl 0168.38801
[12] Reuter, G. E. H., Denumerable Markov processes and the associated contraction semiproups onl, Acta Math., 97, 1-46 (1957) · Zbl 0079.34703
[13] Reuter, G. E. H., Denumerable Markov processes (II), J. London Math. Soc., 34, 81-91 (1959) · Zbl 0089.13803
[14] Reuter, G. E. H., Denumerable Markov processes (III), J. London Math. Soc., 37, 63-73 (1962) · Zbl 0114.33604
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