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Uniform bounds under increment conditions
Author:
Michel Weber
Journal:
Trans. Amer. Math. Soc. 358 (2006), 911-936
MSC (2000):
Primary 60F99; Secondary 28D99
Posted:
June 9, 2005
MathSciNet review:
2177045
Full-text PDF Free Access
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Additional Information
Abstract: We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.
References
- [B]
Berkes I. (private communication).
- [BW]
Boukhari F., Weber M. [2002] Almost sure convergence of weighted series of contractions, Illinois J. Math. 46 no. 1, p. 1-21. MR 1936072 (2004b:28023)
- [CL]
Cohen G., Lin M. [2002] Laws of large numbers with rates and the one-sided ergodic Hilbert transform, Illinois J. Math. 47 (2003), 997-1031. MR 2036987 (2005a:47014)
- [DL]
Derriennic Y., Lin M. [2001] Fractional Poisson equations and ergodic theorems for fractional coboundaries, Israël J. Math. 123 p. 93-130. MR 1835290 (2002f:47017)
- [Ga]
Gaposhkin V.F. [1981] On the dependence of the convergence rate in the SLLN for stationary processes on the rate of decay of the correlation function, Theory Prob. and its Appl. 26 p. 706-720.MR 0636767 (83d:60040)
- [GK]
Gál I.S., Koksma J.F. [1950] Sur l'ordre de grandeur des fonctions sommables, Indag. Math. 12 p. 192-207.MR 0036291 (12:86b)
- [K]
Krengel U. [1985] Ergodic Theorems, Walters de Gruyter & Co, Berlin.MR 0797411 (87i:28001)
- [LW]
Lifshits M., Weber M. [2000] Spectral Regularization Inequalities, Math. Scand. 86 p. 75-99.MR 1738516 (2001b:47018)
- [S]
Schneider D. [1997] Théorèmes ergodiques perturbés, Israël J. Math. 101 p. 157-178.MR 1484874 (99c:28056)
- [Tal1]
Talagrand M. [1996] Convergence of Orthogonal Series Using Stochastic Processes (http: //www.math.ohio-state.edu/ talagran/preprints).
- [Tal2]
Talagrand M. [1993] Sample boundedness of stochastic processes under increment conditions, Ann. Probab. 18, p. 1-49.MR 1043935 (91f:60078)
- [Tan]
Tandori K. [1957] Zur Divergenz der Orthogonal Reihe, Acta Sci. Math. Szeged 18 p. 57-130.
- [W1]
Weber M. [2000] Estimating Random Polynomials by means of Metric Entropy Methods, Mathematical Inequ. & Appl. 3 no. 3, p. 443-457. MR 1768824 (2001m:60084)
- [W2]
Weber M. [2000] Some theorems related to almost sure convergence of orthogonal series, Indag. Math. (N.S.) 11 no. 2, p. 293-311.MR 1813729 (2001k:60047)
- [W3]
Weber M. [2004] Some examples of application of the metric entropy method, Acta Math. Hungar. 105, no. 1-2, 39-83. MR 2093929
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Additional Information
Michel Weber
Affiliation:
Mathématique (IRMA), Université Louis-Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex, France
Email:
weber@math.u-strasbg.fr
DOI:
http://dx.doi.org/10.1090/S0002-9947-05-03805-5
PII:
S 0002-9947(05)03805-5
Keywords:
Almost sure convergence,
majorizing measure,
maximal inequality,
G\'al-Koksma inequality,
ergodic sums
Received by editor(s):
March 29, 2003
Received by editor(s) in revised form:
April 21, 2004
Posted:
June 9, 2005
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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