A sharp correlation inequality with application to almost sure local limit theorem

• Autorzy: Weber M.
• Języki publikacji: EN

Abstrakty

EN

We prove a new sharp correlation inequality for sums of i.i.d. square integrable lattice distributed random variables. We also apply it to establish an almost sure version of the local limit theorem for i.i.d. square integrable random variables taking values in an arbitrary lattice. This extends a recent similar result jointly obtained with Giuliano-Antonini under a slightly stronger absolute moment assumption (of order 2+u with u > 0). The approach used to treat the case u > 0 breaks down when u = 0. Mac- Donald’s concept of the Bernoulli part of a random variable is used in a crucial way to remedy this.

Słowa kluczowe

EN

correlation inequality; i.i.d. random variables; lattice distributed; Bernoulli part; square integrable; local limit theorem; almost sure version

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 1
• Strony: 79--98
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Weber M.

• C.N.R.S. IRMA, Université Louis-Pasteur, 7 rue René Descartes, 67084-Strasbourg Cedex, France

Bibliografia

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• [3] R. Giuliano-Antonini and M. Weber, The intersective ASCLT, Stochastic Anal. Appl. 22 (4) (2004), pp. 1009-1025.
• [4] R. Giuliano-Antonini and M. Weber, Almost sure local limit theorems with rate, inrevision to Stochastic Anal. Appl.
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• [7] M. Kac, R. Salem and A. Zygmund, A gap theorem, Trans. Amer. Math. Soc. 63 (1948), pp. 235-243.
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• [12] M. Weber, On representation of integers, submitted to publication.