Abstract
We study Davis' series of moderate deviations probabilities for
Open Access
Moderate deviations for bounded subsequences
Received08 Dec 2005
Revised14 Apr 2006
Accepted21 Apr 2006
Published05 Sept 2006
References
D. J. Aldous, “Limit theorems for subsequences of arbitrarily-dependent sequences of random variables,” Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 40, no. 1, pp. 59–82, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Asmussen and T. G. Kurtz, “Necessary and sufficient conditions for complete convergence in the law of large numbers,” The Annals of Probability, vol. 8, no. 1, pp. 176–182, 1980.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. Berkes and E. Péter, “Exchangeable random variables and the subsequence principle,” Probability Theory and Related Fields, vol. 73, no. 3, pp. 395–413, 1986.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. D. Chatterji, “A general strong law,” Inventiones Mathematicae, vol. 9, no. 3, pp. 235–245, 1970.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. D. Chatterji, “A principle of subsequences in probability theory: the central limit theorem,” Advances in Mathematics, vol. 13, no. 1, pp. 31–54, 1974.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. D. Chatterji, “A subsequence principle in probability theory. II. The law of the iterated logarithm,” Inventiones Mathematicae, vol. 25, no. 3-4, pp. 241–251, 1974.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Davis, “Convergence rates for probabilities of moderate deviations,” Annals of Mathematical Statistics, vol. 39, pp. 2016–2028, 1968.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Davis, “Convergence rates for the law of the iterated logarithm,” Annals of Mathematical Statistics, vol. 39, pp. 1479–1485, 1968.
View at: Google Scholar | Zentralblatt MATH | MathSciNetN. Dunford and J. T. Schwartz, Linear Operators. Part I. General Theory, Wiley Classics Library, John Wiley & Sons, New York, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Gut, “Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices,” The Annals of Probability, vol. 8, no. 2, pp. 298–313, 1980.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Gut, “On complete convergence in the law of large numbers for subsequences,” The Annals of Probability, vol. 13, no. 4, pp. 1286–1291, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Loève, Probability Theory. I, vol. 45 of Graduate Texts in Mathematics, Springer, New York, 4th edition, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Spătaru, “On a series concerning moderate deviations,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 45, no. 5, pp. 883–896 (2001), 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetG. Stoica, “Davis-type theorems for martingale difference sequences,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2005, no. 2, pp. 159–165, 2005.
View at: Publisher Site | Google Scholar | MathSciNetG. Stoica, “Series of moderate deviation probabilities for martingales,” Journal of Mathematical Analysis and Applications, vol. 308, no. 2, pp. 759–763, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 George Stoica. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.