Strong ratio limit theorems for mixing Markov operators

Michael Lin

Annales de l'I.H.P. Probabilités et statistiques (1976)

  • Volume: 12, Issue: 2, page 181-191
  • ISSN: 0246-0203

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Lin, Michael. "Strong ratio limit theorems for mixing Markov operators." Annales de l'I.H.P. Probabilités et statistiques 12.2 (1976): 181-191. <http://eudml.org/doc/77041>.

@article{Lin1976,
author = {Lin, Michael},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {2},
pages = {181-191},
publisher = {Gauthier-Villars},
title = {Strong ratio limit theorems for mixing Markov operators},
url = {http://eudml.org/doc/77041},
volume = {12},
year = {1976},
}

TY - JOUR
AU - Lin, Michael
TI - Strong ratio limit theorems for mixing Markov operators
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1976
PB - Gauthier-Villars
VL - 12
IS - 2
SP - 181
EP - 191
LA - eng
UR - http://eudml.org/doc/77041
ER -

References

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  1. [1] S.R. Foguel, The ergodic theory of Markov processes. Van NostrandMathematical Studies21. New York, Van NostrandReinhold, 1969. Zbl0282.60037MR261686
  2. [2] S.R. Foguel, On iterates of convolutions. Proc. Amer. Math. Soc., t. 47, 1975, p. 368- 370. Zbl0299.43004MR374816
  3. [3] S.R. Foguel and M. Lin, Some ratio limit theorems for Markov operators. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 23, 1972, p. 55-66. Zbl0223.60027MR310974
  4. [4] S. Horowitz, Transition probabilities and contractions of L∞. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 24, 1972, p. 263-274. Zbl0228.60028MR331516
  5. [5] S. Horowitz, On σ-finite invariant measures for Markov processes. Israel J. Math., t. 6, 1968, p. 338-345. Zbl0176.47804MR243610
  6. [6] N.C. Jain, The strong ratio limit property for some general Markov processes. Ann. Math. Stat., t. 40, 1969, p. 986-992. Zbl0194.49601MR245086
  7. [7] B. Jamison and S. Orey, Markov chains recurrent in the sense of Harris. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 8, 1967, p. 41-48. Zbl0153.19802MR215370
  8. [8] U. Krengel and L. Sucheston, On mixing in infinite measure spaces. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 13, 1969, p. 150-164. Zbl0176.33804MR254215
  9. [9] M.L. Levitan, Some ratio limit theorems for a general space state Markov process. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 15, 1970, p. 29-50. Zbl0192.55202MR281257
  10. [10] M.L. Levitan and L.H. Smolowitz, Limit theorems for reversible Markov processes. Ann. Prob., t. 1, 1973, p. 1014-1025. Zbl0271.60068MR353452
  11. [11] M. Lin, Strong ratio limit theorems for Markov Processes. Ann. Math. Stat., t. 43, 1972, p. 569-579. Zbl0243.60039MR315787
  12. [12] M. Lin, Convergence of the iterates of a Markov operator. Z. Wahrscheinlichkeitstheorie Verw. Geb., t. 29, 1974, p. 153-163. Zbl0269.60057MR365714
  13. [13] D. Ornstein and L. Sucheston, An operator theorem on L1 convergence to zero with applications to Markov kernels. Ann. Math. Stat., t. 41, 1970, p. 1631-1639. Zbl0284.60068MR272057
  14. [14] W. Pruitt, Strong ratio limit property for R-recurrent Markov chains. Proc. Amer. Math. Soc., t. 16, 1965, p. 196-200. Zbl0131.16603MR174089
  15. [15] C. Stone, Ratio limit theorems for random walks on groups. Trans. Amer. Math. Soc., t. 125, 1966, p. 86-100. Zbl0168.38501MR217887

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