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Maximal inequalities for demimartingales and a strong law of large numbers

โœ Scribed by Tasos C. Christofides

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
86 KB
Volume
50
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Chow's maximal inequality for (sub)martingales is extended to the case of demi(sub)martingales introduced by Newman and Wright (Z. Wahrsch. Verw. Geb. 59 (1982) 361-371). This result serves as a "source" inequality for other inequalities such as the Hajek-Renyi inequality and Doob's maximal inequality and leads to a strong law of large numbers. The partial sum of mean zero associated random variables is a demimartingale. Therefore, maximal inequalities and a strong law of large numbers are obtained for associated random variables as special cases.

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## a b s t r a c t In this work, we establish an exponential inequality for unbounded negatively orthant dependent (NOD) random variables. The inequality extends and improves the results of [1], [2], and Xing et al. (2009) [3]. We also obtain the convergence rate O(n -1/2 ln 1/2 n) for the stron