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An exponential inequality for a NOD sequence and a strong law of large numbers

✍ Scribed by Xuejun Wang; Shuhe Hu; Aiting Shen; Wenzhi Yang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
219 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

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 strong law of large numbers, which improves on the corresponding ones of [1], Nooghabi and Azarnoosh (2009) [2], and Xing et al. (2009) [3].

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Maximal inequalities for demimartingales
Maximal inequalities for demimartingales and a strong law of large numbers
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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 inequali