Sur la propriété de la limite centrale dans 𝒟 [ 0 , 1 ]

Paul Hubert Bézandry; Xavier Fernique

Annales de l'I.H.P. Probabilités et statistiques (1992)

  • Volume: 28, Issue: 1, page 31-46
  • ISSN: 0246-0203

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Bézandry, Paul Hubert, and Fernique, Xavier. "Sur la propriété de la limite centrale dans ${\mathcal {D}} [ 0, 1 ]$." Annales de l'I.H.P. Probabilités et statistiques 28.1 (1992): 31-46. <http://eudml.org/doc/77423>.

@article{Bézandry1992,
author = {Bézandry, Paul Hubert, Fernique, Xavier},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {cadlag processes; complete metric space; central limit theorem},
language = {fre},
number = {1},
pages = {31-46},
publisher = {Gauthier-Villars},
title = {Sur la propriété de la limite centrale dans $\{\mathcal \{D\}\} [ 0, 1 ]$},
url = {http://eudml.org/doc/77423},
volume = {28},
year = {1992},
}

TY - JOUR
AU - Bézandry, Paul Hubert
AU - Fernique, Xavier
TI - Sur la propriété de la limite centrale dans ${\mathcal {D}} [ 0, 1 ]$
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1992
PB - Gauthier-Villars
VL - 28
IS - 1
SP - 31
EP - 46
LA - fre
KW - cadlag processes; complete metric space; central limit theorem
UR - http://eudml.org/doc/77423
ER -

References

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  1. [1] P.H. Bézandry et X. Fernique, Analyse de fonctions aléatoires peu régulières sur [0,1], C. R. Acad. Sci.Paris, t. 310, série I, 1990, p. 745-750. Zbl0707.60036MR1055241
  2. [2] P. Billingsley, Convergence of Probability Measures, J. Wiley, New York, 1968. Zbl0172.21201MR233396
  3. [3] N.N. Censov, Weak Convergence of Stochastic Processes whose Trajectories Have no Discontinuities of the Secund Order, Theory Prob. Appl., vol. 1-3, 1956, p. 140-149. 
  4. [4] X. Fernique, Régularité de fonctions aléatoires non gaussiennes, Springer Lect. Notes Math., n° 976, p. 1-74. Zbl0507.60027MR722982
  5. [5] I.I. Gihman et A.V. Skorohod, The Theory of Stochastic Processes, I, Berlin-Heidelberg-New York, Springer, 1974. Zbl0291.60019MR346882
  6. [6] E. Giné et J. Zinn, Lectures on the Central Limit Theorem for Empirical Processes, Lect. Notes Math., vol. 1221, p. 50-113, Berlin, Heidelberg, New York, Springer, 1986. Zbl0605.60026MR875007
  7. [7] M.G. Hahn, Central Limit Theorems in D ([0, 1]), Z. Wahr verw. Gebiete, vol. 44, 1978, p. 89-101. Zbl0378.60002MR501231
  8. [8] D. Jukneviciene, Central Limit Theorem in the Space D[0,1], Lithuanian Math. J., vol. 25, 1985, p. 293-298. Zbl0593.60032MR823656
  9. [9] M.B. Marcus et G. Pisier, Characterisation of Alsmost Surely Continuous p-Stable Random Fourier Series and Strongly Stationary Processes, Acta Math., vol. 152, 1984, p. 245-301. Zbl0547.60047MR741056
  10. [10] V. Paulauskas et Ch. Stieve, On the Central Limit Theorem in D ([0, 1]) and D([0,1); H), Lietuvos Matematikos Rinkings, vol. 30, 1990, p. 267-276. Zbl0722.60023MR1082482
  11. [11] G. Pisier, Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique, Sém. d'Anal. Fonct., 1979–1980, exposés 13-14, Paris, École Polytechnique. Zbl0441.60040MR604395
  12. [12] R. Ranga Rao, The Law of Large Numbers for D([0, 1])-Valued Random Variables, Theory Prob. Appl., vol. 8, 1963, p. 70-74. Zbl0122.13303
  13. [13] A.V. Skorohod, Limit Theorem for Stochastic Processes, Theory Prob. Appl., vol. 1- 3, 1956, p. 261-290. 

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