On the rate of convergence in the central limit theorem for martingale difference sequences

Lahcen Ouchti

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 1, page 35-43
  • ISSN: 0246-0203

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Ouchti, Lahcen. "On the rate of convergence in the central limit theorem for martingale difference sequences." Annales de l'I.H.P. Probabilités et statistiques 41.1 (2005): 35-43. <http://eudml.org/doc/77836>.

@article{Ouchti2005,
author = {Ouchti, Lahcen},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Central limit theorem; Martingale difference sequence; Rate of convergence},
language = {eng},
number = {1},
pages = {35-43},
publisher = {Elsevier},
title = {On the rate of convergence in the central limit theorem for martingale difference sequences},
url = {http://eudml.org/doc/77836},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Ouchti, Lahcen
TI - On the rate of convergence in the central limit theorem for martingale difference sequences
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 1
SP - 35
EP - 43
LA - eng
KW - Central limit theorem; Martingale difference sequence; Rate of convergence
UR - http://eudml.org/doc/77836
ER -

References

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  1. [1] A.C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc.49 (1941) 122-136. Zbl0025.34603MR3498JFM67.0461.01
  2. [2] P. Billingsley, Convergence of Probability Measures, Wiley, 1968. Zbl0172.21201MR233396
  3. [3] E. Bolthausen, Exact convergence rates in some martingale central limit theorems, Ann. Probab.10 (3) (1982) 672-688. Zbl0494.60020MR659537
  4. [4] M. El Machkouri, D. Volný, On the central and local limit theorems for martingale difference sequences, Stochastics and Dynamics, submitted for publication. Zbl1080.60015MR2069687
  5. [5] C.G. Esseen, On the Liapounoff limit of error in the theory of probability, Ark. Math. Astr. och Fysik A28 (1942) 1-19. Zbl0027.33902MR11909JFM68.0277.02
  6. [6] B.V. Gnedenko, A.N. Kolomogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA, 1954, translated by K.L. Chung. Zbl0056.36001MR62975
  7. [7] W.F. Grams, Rate of convergence in the central limit theorem for dependent variables, Dissertation, Florida State Univ., 1972. 
  8. [8] E. Haeusler, On the rate of convergence in the central limit theorem for martingales with discrete and continuous time, Ann. Probab.16 (1) (1988) 275-299. Zbl0639.60030MR920271
  9. [9] T. Nakata, On the rate of convergence in mean central limit theorem for martingale differences, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs.23 (1976) 10-15. Zbl0372.60063MR451362
  10. [10] P. Hall, C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York, 1980. Zbl0462.60045MR624435
  11. [11] I.A. Ibragimov, A central limit theorem for a class of dependent random variables, Theory Probab. Appl.8 (1963) 83-89. Zbl0123.36103MR151997
  12. [12] Y. Kato, Rates of convergence in central limit theorem for martingale differences, Bull. Math. Statist.18 (1979) 1-8. Zbl0401.60018MR517156
  13. [13] M. Loève, Probability Theory, D. Van Nostrand, Princeton, NJ, 1955. Zbl0108.14202MR123342

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