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Almost sure central limit theorem for strictly stationary processes
Author(s):
Emmanuel
Lesigne
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1751-1759.
MSC (1991):
Primary 28D05, 60G10, 60F05
Posted:
September 30, 1999
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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:
- 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.
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- 7.
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- 8.
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- 9.
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- 11.
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- 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)
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Additional Information:
Emmanuel
Lesigne
Affiliation:
Département de Mathématiques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France
Email:
lesigne@univ-tours.fr
DOI:
10.1090/S0002-9939-99-05157-6
PII:
S 0002-9939(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
Posted:
September 30, 1999
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
2000,
American Mathematical Society
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