The functional central limit theorem for strongly mixing processes

Paul Doukhan; Pascal Massart; Emmanuel Rio

Annales de l'I.H.P. Probabilités et statistiques (1994)

  • Volume: 30, Issue: 1, page 63-82
  • ISSN: 0246-0203

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Doukhan, Paul, Massart, Pascal, and Rio, Emmanuel. "The functional central limit theorem for strongly mixing processes." Annales de l'I.H.P. Probabilités et statistiques 30.1 (1994): 63-82. <http://eudml.org/doc/77475>.

@article{Doukhan1994,
author = {Doukhan, Paul, Massart, Pascal, Rio, Emmanuel},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Donsker-Prokhorov invariance principle; strictly stationary; strongly mixing sequence; strong mixing function; functional central limit theorem},
language = {eng},
number = {1},
pages = {63-82},
publisher = {Gauthier-Villars},
title = {The functional central limit theorem for strongly mixing processes},
url = {http://eudml.org/doc/77475},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Doukhan, Paul
AU - Massart, Pascal
AU - Rio, Emmanuel
TI - The functional central limit theorem for strongly mixing processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 1
SP - 63
EP - 82
LA - eng
KW - Donsker-Prokhorov invariance principle; strictly stationary; strongly mixing sequence; strong mixing function; functional central limit theorem
UR - http://eudml.org/doc/77475
ER -

References

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  1. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. Zbl0172.21201MR233396
  2. R. Bradley, Basic Properties of Strong Mixing Conditions, Dependence in Probability and Statistics. A Survey of Recent Results, Oberwolfach, 1985, E. EBERLEIN and M. S. TAQQU Ed., Birkhäuser, 1986. Zbl0603.60034MR899990
  3. A. Bulinskii and P. Doukhan, Inégalités de mélange fort utilisant des normes d'Orlicz, C. R. Acad. Sci. Paris, Série I, Vol. 305, 1987, pp. 827-830. Zbl0659.60009MR923208
  4. Y.A. Davydov, Convergence of Distributions Generated by Stationary Stochastic Processes, Theor. Probab. Appl., Vol. 13, 1968, pp. 691-696. Zbl0181.44101
  5. Y.A. Davydov, Mixing Conditions for Markov Chains, Theor. Probab. Appl., Vol. 18, 1973, pp. 312-328. Zbl0297.60031MR321183
  6. A. Dellacherie and P.A. Meyer, Probabilité et potentiel, Masson, Paris, 1975. Zbl0323.60039
  7. P. Doukhan, Mixing: Properties and Examples, Preprint, Université de Paris-Sud, 91-60, 1991. MR1312160
  8. W. Feller, An Introduction to probability Theory and its Applications, Wiley, New York, 1950. Zbl0039.13201MR38583
  9. M.I. Gordin, The Central Limit Theorem for Stationary Processes, Soviet Math. Dokl., Vol. 10, 1969, pp. 1174-1176. Zbl0212.50005MR251785
  10. P. Hall and C.C. Heyde, Martingal Limit Theory and its Application, North-Holland, New York, 1980. Zbl0462.60045MR624435
  11. N. Herrndorf, A Functional Central Limit Theorem for Strongly Mixing Sequences of Random Variables, Z. Wahr. Verv. Gebiete, Vol. 69, 1985, pp. 541-550. Zbl0558.60032MR791910
  12. I. A. Ibragimov, Some Limit Theorems for Stationary Processes, Theor. Probab. Appl., Vol. 7, 1962, pp. 349-382. Zbl0119.14204MR148125
  13. I Bragimov and Y.V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Amsterdam, 1971. Zbl0219.60027MR322926
  14. H. Oodaira and K.I. Yoshihara, Functional Central Limit Theorems for strictly Stationary Processes Satisfying the Strong Mixing Condition, Kodai Math. Sem. Rep., Vol. 24, 1972, pp. 259-269. Zbl0245.60006MR317380
  15. M. Peligrad, Recent Advances in the Central Limit Theorem and its Weak Invariance Principles for Mixing Sequences of Random variables, Dependence in Probability and Statistics. A Survey of Recent Results, Oberwolfach, 1985, E. EBERLEIN and M. S. TAQQU Eds., Birkhäuser, 1986. Zbl0603.60022MR899991
  16. E. Rio, Covariance Inequalities for Strongly Mixing Processes, Preprint, Université de Paris- Sud, 1992. 
  17. M. Rosenblatt, A Central Limit Theorem and a Strong Mixing Condition, Proc. Nat. Acad. Sci. U.S.A., Vol. 42, 1956, pp. 43-47. Zbl0070.13804MR74711
  18. Y.A. Rozanov and V.A. Volkonskii, Some Limit Theorems for Random Functions I, Theory Probab. Appl., Vol. 4, 1959, pp. 178-197. Zbl0092.33502MR121856
  19. V. Strassen, A Converse to the Law of the Iterated Logarithm, Z. Wahr. Verv. Gebiete, Vol. 4, 1966, pp. 265-268. Zbl0141.16501MR200965

Citations in EuDML Documents

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  1. Martial Longla, On dependence structure of copula-based Markov chains
  2. Karine Tribouley, Gabrielle Viennet, L p adaptive density estimation in a β mixing framework
  3. Emmanuel Rio, Covariance inequalities for strongly mixing processes
  4. Emmanuel Rio, About the Lindeberg method for strongly mixing sequences
  5. P. Doukhan, P. Massart, E. Rio, Invariance principles for absolutely regular empirical processes
  6. Jérôme Dedecker, Emmanuel Rio, On the functional central limit theorem for stationary processes
  7. Jérôme Dedecker, Florence Merlevède, Magda Peligrad, A quenched weak invariance principle

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