×

Sur la frontière de Martin des processus de Markov à temps discret. (French) Zbl 0273.60042


MSC:

60J05 Discrete-time Markov processes on general state spaces
47A35 Ergodic theory of linear operators
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] M.A. Akcoglu , An ergodic lemma . Proc. Amer. Math. Soc. , t. 16 , 1965 , p. 388 - 392 . MR 179325 | Zbl 0134.12103 · Zbl 0134.12103 · doi:10.2307/2034660
[2] M.A. Akcoglu et R.W. Sharpe , Ergodic Theory and Boundaries . Trans. Amer. Math. Soc. , 1968 , p. 447 - 460 . MR 224770 | Zbl 0162.19402 · Zbl 0162.19402 · doi:10.2307/1994852
[3] R. Azencott , Marches aléatoires sur les groupes localement compacts . C. R. Acad. Sci. Paris , t. 268 , 1969 , p. 1406 - 1409 . MR 268969 | Zbl 0214.15802 · Zbl 0214.15802
[4] A. Brunel , Sur un lemme ergodique voisin du lemme de E. Hopf et sur une de ses applications . C. R. Acad. Sci. Paris , t. 256 , 1963 , p. 5481 - 5484 . MR 152633 | Zbl 0117.10402 · Zbl 0117.10402
[5] R.V. Chacon , Identification of the limit of operator averages . J. Math. Mech. , t. 11 , 1962 , p. 961 - 968 . MR 145352 | Zbl 0139.34701 · Zbl 0139.34701
[6] R.V. Chacon et D.S. Ornstein , A general ergodic theorem . Illinois J. Math. , t. 4 , 1960 , p. 153 - 160 . Article | MR 110954 | Zbl 0134.12102 · Zbl 0134.12102
[7] J.L. Doob , Discrete potential theory and boundaries . J. Math. Mech. , t. 8 , 1959 , p. 433 - 458 . MR 107098 | Zbl 0101.11503 · Zbl 0101.11503
[8] J.L. Doob , A ratio operator limit theorem . Z. für Wahrschein 1 , 1963 , p. 288 - 294 . MR 163333 | Zbl 0122.36302 · Zbl 0122.36302 · doi:10.1007/BF00532502
[9] N. Dunford et J.T. Schwartz , Linear Operators , Part I, Interscience Publ. , 1958 . MR 117523 | Zbl 0084.10402 · Zbl 0084.10402
[10] E.B. Dynkin , Boundary theory of Markov processes (the discrete case). Russian Math. Surveys , t. 24 , 1969 , n^\circ 2 . MR 245096 | Zbl 0222.60048 · Zbl 0222.60048 · doi:10.1070/RM1969v024n02ABEH001341
[11] J. Feldman , Feller and Martin boundaries for countable sets . Illinois J. Math. , t. 6 , 1962 , p. 356 - 366 . Article | MR 139202 | Zbl 0106.33402 · Zbl 0106.33402
[12] W. Feller , Boundaries induced by non negative matrices . Trans. Amer. Math. Soc. , t. 83 , 1956 , p. 19 - 54 . MR 90927 | Zbl 0071.34901 · Zbl 0071.34901 · doi:10.2307/1992904
[13] G.A. Hunt , Markoff chains and Martin boundaries . Illinois J. Math. , t. 4 , 1960 , p. 313 - 340 . Article | MR 123364 | Zbl 0094.32103 · Zbl 0094.32103
[14] J.G. Kemeny , Denumerable Markov Chains . J. L. SNELL et A. W. KNAPP, Van Nostrand , 1966 . MR 207042 | Zbl 0149.13301 · Zbl 0149.13301
[15] R.S. Martin , Minimal positive harmonic functions . Trans. Amer. Math. Soc. , t. 49 , 1941 , p. 137 - 172 . MR 3919 | Zbl 0025.33302 | JFM 67.0343.03 · Zbl 0025.33302 · doi:10.2307/1990054
[16] J. Neveu , Bases mathématiques du Calcul des Probabilités , Masson ( Paris ), 1964 . MR 198504 | Zbl 0137.11203 · Zbl 0137.11203
[17] J. Neveu , Chaînes de Markov et théorie du potentiel . Ann. Fac. des Sciences de Clermont , t. 24 , 1964 p. 37 - 89 . Numdam | MR 386031
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.