Quasi-compactness and uniform ergodicity of Markov operators
Lin, Michael
Annales de l'I.H.P. Probabilités et statistiques, Tome 11 (1975), p. 345-354 / Harvested from Numdam
@article{AIHPB_1975__11_4_345_0,
     author = {Lin, Michael},
     title = {Quasi-compactness and uniform ergodicity of Markov operators},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {11},
     year = {1975},
     pages = {345-354},
     mrnumber = {402007},
     zbl = {0318.60065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1975__11_4_345_0}
}
Lin, Michael. Quasi-compactness and uniform ergodicity of Markov operators. Annales de l'I.H.P. Probabilités et statistiques, Tome 11 (1975) pp. 345-354. http://gdmltest.u-ga.fr/item/AIHPB_1975__11_4_345_0/

[1] A. Brunel, Chaines abstraites de Markov vérifiant une condition de Orey. Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 19, 1971, p. 323-329. | MR 317410 | Zbl 0203.50305

[2] A. Brunel and D. Revuz, Quelques applications probabilistes de la quasi-compacité. Ann. Inst. H. Poincaré (sect. B), t. 10, 1974, p. 301-337. | Numdam | MR 373008 | Zbl 0318.60064

[3] W. Doeblin, Sur les propriétés asymptotiques de mouvements régis par certains types de chaines simples. Bull. Math. Soc. Roum. Sci., t. 39, 1937, n° 1, p. 57-115 ; n° 2, p. 3-61. | JFM 63.1077.03 | Zbl 0019.17503

[4] J.L. Doob, Stochastic Processes. Wiley, New York, 1953. | MR 58896 | Zbl 0053.26802

[5] N. Dunford and J.T. Schwartz, Linear operators. Part I. Interscience, New York, 1958. | MR 117523 | Zbl 0084.10402

[6] S.R. Foguel, Ergodic theory of Markov processes. Van-Nostrand, New York, 1969. | MR 261686 | Zbl 0282.60037

[7] S.R. Foguel and B. Weiss, On convex power series of a conservative Markov operator. Proc. Amer. Math. Soc., t. 38, 1973, p. 325-330. | MR 313476 | Zbl 0268.47014

[8] S. Horowitz, Transition probabilities and contractions of L∞. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, t. 24, 1972, p. 263-274. | MR 331516 | Zbl 0228.60028

[9] M. Lin, On quasi-compact Markov operators. Ann. Prob., t. 2, 1974, p. 464-475. | MR 368148 | Zbl 0285.28019

[10] M. Lin, On the uniform ergodic theorem. Proc. Amer. Math. Soc., t. 43, 1974, p. 337-340. | MR 417821 | Zbl 0252.47004

[11] M. Lin, On the uniform ergodic theorem, II. Proc. Amer. Math. Soc., t. 46, 1974, p. 217-225. | MR 417822 | Zbl 0291.47006

[12] S.T.C. Moy, Period of an irreducible operator. Illinois J. Math., t. 11, 1967, p. 24-39. | MR 211470 | Zbl 0171.16104

[13] J. Neveu, Mathematical Foundations of the Calculus of Probability. Holden-day, San Francisco, 1965. | MR 198505 | Zbl 0137.11301

[14] I. Sawashima and F. Niiro, Reduction of a Sub-Markov operator to its irreducible components. Nat. Sci. Rep. of Ochakomizu University, t. 24, 1973, p. 35-59. | MR 343065 | Zbl 0281.47021

[15] H.H. Schaefer, Invariant ideals of positive operators in C(X). Illinois J. Math., t. 11, 1967, p. 703-715. | MR 218912 | Zbl 0168.11801

[16] K. Yosida and S. Kakutani, Operator theoretical treatment of Markoff's process and mean ergodic theorem. Ann. of Math. (2), t. 42, 1941, p. 188-228. | JFM 67.0417.01 | MR 3512 | Zbl 0024.32402