Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive

Nelly Maigret

Annales de l'I.H.P. Probabilités et statistiques (1978)

  • Volume: 14, Issue: 4, page 425-440
  • ISSN: 0246-0203

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Maigret, Nelly. "Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive." Annales de l'I.H.P. Probabilités et statistiques 14.4 (1978): 425-440. <http://eudml.org/doc/77102>.

@article{Maigret1978,
author = {Maigret, Nelly},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {functional central limit theorem; positive recurrent Harris chain; martingale convergence theorems; Wiener process; Doeblin recurrent},
language = {fre},
number = {4},
pages = {425-440},
publisher = {Gauthier-Villars},
title = {Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive},
url = {http://eudml.org/doc/77102},
volume = {14},
year = {1978},
}

TY - JOUR
AU - Maigret, Nelly
TI - Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1978
PB - Gauthier-Villars
VL - 14
IS - 4
SP - 425
EP - 440
LA - fre
KW - functional central limit theorem; positive recurrent Harris chain; martingale convergence theorems; Wiener process; Doeblin recurrent
UR - http://eudml.org/doc/77102
ER -

References

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  1. [1] Aleskeviscus, Some limit theorems for sums of random variables defined on a homogenous regular Markov chain (Russian). Litovsk. Math. Sb., t. 6, 1966, p. 297-311. MR220344
  2. [2] P. Billingsley, Convergence of probability measures. John Wiley, 1968. Zbl0172.21201MR233396
  3. [3] E. Bolthausen, On rates of convergence in a randon central limit theorem and in the central limit for Markov chains. Warscheinlichkeitstheorie verw-gebiete, t. 38, 1977, p. 279-286. Zbl0336.60060MR482943
  4. [4 a] R. Cogburn, The central limit theorem for Markov processes. Six Berkeley symposium in probabilities, 1972. Zbl0318.60017
  5. [4 b] Cogburn, A uniform theory for sums of Markov chain transition probabilities. Ann. Prob., vol. 3, n° 2, 1975, p. 191-214. Zbl0348.60106MR378103
  6. [5] L. Landers, Rogg, On the rate of convergence in the central limit theorem for Markov chains. Z. Wahrscheinlichkeitstheorie verw-gebiete, t. 35, 1976, p. 57-63. Zbl0315.60014MR407938
  7. [6] Mandl, Estimation and control in Markov chains. Advanced applied probabilities, t. 6, 1974, p. 40-60. Zbl0281.60070MR339876
  8. [7] Neveu, Potentiel markovien récurrent des chaînes de Harris. Ann. Inst. Fourier, t. 22 (2), p. 85-130. Zbl0226.60084MR380992
  9. [8] Numelin, a) A splitting technique for φ recurrent Markov chains ; b) On the Poisson equation for φ recurrent Markov chains (à paraître). 
  10. [9] Orey, Limit theorems for Markov chains transition probabilities. Van Nostrand, 1971. Zbl0295.60054
  11. [10] G.H. Popescu, A functional central limit theorem for a class of Markov chains. Revue roumaine, math. pures et appliquées, t. 21, n° 6, 1976, p. 737-750. Bucarest. Zbl0343.60045MR415730
  12. [11] B.L.S. Prakasa Rao, a) On the rate of convergence of estimations for Markov processes. Wahrscheinlichkeitstheorie verw-gebiete, t. 26, 1973, p. 141-152 ; b) Remark on the rate of convergence in the random central limit theorem for mixing sequences. Wahrscheinlichkeitstheorie verw-gebiete, t. 31, 1975, p. 157-160. Springer Verlag. Zbl0306.60011MR339420
  13. [12] R. Rebolledo, a) Remarque sur la convergence en loi des martingales vers des martingales continues II. C. R. Acad. Sci. Paris (séance du 12 septembre 1977); b) La méthode des martingales appliquée à l'étude de la convergence en loi de processus. A paraître. MR461626
  14. [13] D. Revuz, Markov chains, North Holland, 1975. Zbl0332.60045MR415773
  15. [14] Saulis, Statuljavicus, An asymptotic expansion for the probabilities of large deviations of sums of random variables that are connected in a Markov chain. Litovsk. Math. Sb, t. 10, 1960, p. 359-366. MR273669
  16. [15] Statuljavicus, Limit theorems for sums of random variables that are connected in a Markov chain. I, II, III. Litovsk. Math. Sb, t. 9, 1969, p. 345-362 ; t. 9, 1969, p. 635-672 ; t. 10, 1970, p. 161-169. MR266281
  17. [16] Stone, Weak convergence of stochastic processes defined on semi infinite intervals. Proc. A. M. S., vol. 14, 1963. Zbl0116.35602

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