Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Almost sure central limit theorem
for strictly stationary processes


Author: Emmanuel Lesigne
Journal: Proc. Amer. Math. Soc. 128 (2000), 1751-1759
MSC (1991): Primary 28D05, 60G10, 60F05
DOI: https://doi.org/10.1090/S0002-9939-99-05157-6
Published electronically: September 30, 1999
MathSciNet review: 1641132
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: On any aperiodic measure preserving system, there exists a square integrable function such that the associated stationary process satifies the Almost Sure Central Limit Theorem.


References [Enhancements On Off] (What's this?)

  • 1. Atlagh, M. & Weber, M. Une nouvelle loi forte des grands nombres. Convergence in Ergodic Theory and Probability, Eds.:Bergelson/March/Rosenblatt, Walter de Gruyter & Co. (1996) MR 97i:60034
  • 2. Berkes, I & Dehling H. On the almost sure central limit theorem for random variables with infinite variance. J. Theor. Probab. 7, p.667-680. (1994) MR 95g:60041
  • 3. Brosamler, G.A. An almost everywhere central limit theorem. Math. Proc. Cambridge Phil. Soc. 104, p.561-574. (1988) MR 89i:60045
  • 4. Burton, R. & Denker, M. On the central limit theorem for dynamical system. Transactions Amer. Math. Soc. 302, p.715-726. (1987) MR 88i:60039
  • 5. Chung, K.L. : A course in probability theory. (1975)
  • 6. Fisher, A. Convex-invariant means and a pathwise central limit theorem. Advances in Math. 63, p.213-246. (1987) MR 88g:60058
  • 7. Lacey, M. On central limit theorems, modulus of continuity and Diophantine type for irrational rotations. J. d'Analyse Math. 61, p.47-59. (1993) MR 95a:60054
  • 8. Lacey, M. & Philipp, W. A note on the almost sure central limit theorem. Statist. Probab. Letters 9, p.201-205. (1990) MR 91e:60100
  • 9. Lévy, P. : Théorie de l'addition des variables aléatoires (chapitre VIII). (1937)
  • 10. Schatte, P. On strong versions of the central limit theorem. Math. Nachr. 137, p.249-256. (1988) MR 89i:60070
  • 11. Volny, D. On limit theorems and category for dynamical systems. Yokohama Math. J. 38, p.29-35. (1990) MR 92c:28014
  • 12. Volny, D. Invariance principles and Gaussian approximation for strictly stationary processes. Preprint (1996), to be published in Transactions Amer. Math. Soc. CMP 98:13
  • 13. Volny, D. & Weber, M. : personal communication. (1996)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28D05, 60G10, 60F05

Retrieve articles in all journals with MSC (1991): 28D05, 60G10, 60F05


Additional Information

Emmanuel Lesigne
Affiliation: Département de Mathématiques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France
Email: lesigne@univ-tours.fr

DOI: https://doi.org/10.1090/S0002-9939-99-05157-6
Keywords: Almost sure central limit theorem, triangular arrays, stationary processes, measure preserving dynamical systems, approximation by Gaussian processes
Received by editor(s): June 14, 1998
Received by editor(s) in revised form: July 22, 1998
Published electronically: September 30, 1999
Communicated by: Stanley Sawyer
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society