Quasi-compactness and uniform ergodicity of Markov operators

Michael Lin

Annales de l'I.H.P. Probabilités et statistiques (1975)

  • Volume: 11, Issue: 4, page 345-354
  • ISSN: 0246-0203

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Lin, Michael. "Quasi-compactness and uniform ergodicity of Markov operators." Annales de l'I.H.P. Probabilités et statistiques 11.4 (1975): 345-354. <http://eudml.org/doc/77029>.

@article{Lin1975,
author = {Lin, Michael},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {4},
pages = {345-354},
publisher = {Gauthier-Villars},
title = {Quasi-compactness and uniform ergodicity of Markov operators},
url = {http://eudml.org/doc/77029},
volume = {11},
year = {1975},
}

TY - JOUR
AU - Lin, Michael
TI - Quasi-compactness and uniform ergodicity of Markov operators
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1975
PB - Gauthier-Villars
VL - 11
IS - 4
SP - 345
EP - 354
LA - eng
UR - http://eudml.org/doc/77029
ER -

References

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  1. [1] A. Brunel, Chaines abstraites de Markov vérifiant une condition de Orey. Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 19, 1971, p. 323-329. Zbl0203.50305MR317410
  2. [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. Zbl0318.60064MR373008
  3. [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. Zbl0019.17503JFM63.1077.03
  4. [4] J.L. Doob, Stochastic Processes. Wiley, New York, 1953. Zbl0053.26802MR58896
  5. [5] N. Dunford and J.T. Schwartz, Linear operators. Part I. Interscience, New York, 1958. Zbl0084.10402MR117523
  6. [6] S.R. Foguel, Ergodic theory of Markov processes. Van-Nostrand, New York, 1969. Zbl0282.60037MR261686
  7. [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. Zbl0268.47014MR313476
  8. [8] S. Horowitz, Transition probabilities and contractions of L∞. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, t. 24, 1972, p. 263-274. Zbl0228.60028MR331516
  9. [9] M. Lin, On quasi-compact Markov operators. Ann. Prob., t. 2, 1974, p. 464-475. Zbl0285.28019MR368148
  10. [10] M. Lin, On the uniform ergodic theorem. Proc. Amer. Math. Soc., t. 43, 1974, p. 337-340. Zbl0252.47004MR417821
  11. [11] M. Lin, On the uniform ergodic theorem, II. Proc. Amer. Math. Soc., t. 46, 1974, p. 217-225. Zbl0291.47006MR417822
  12. [12] S.T.C. Moy, Period of an irreducible operator. Illinois J. Math., t. 11, 1967, p. 24-39. Zbl0171.16104MR211470
  13. [13] J. Neveu, Mathematical Foundations of the Calculus of Probability. Holden-day, San Francisco, 1965. Zbl0137.11301MR198505
  14. [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. Zbl0281.47021MR343065
  15. [15] H.H. Schaefer, Invariant ideals of positive operators in C(X). Illinois J. Math., t. 11, 1967, p. 703-715. Zbl0168.11801MR218912
  16. [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. Zbl0024.32402MR3512JFM67.0417.01

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