An almost sure central limit theorem for products of sums under association

Yun-Xia Li and Jian-Feng Wang

Statistics & Probability Letters, 2008, vol. 78, issue 4, 367-375

Abstract: Let {Xn,n[greater-or-equal, slanted]1} be a strictly stationary positively or negatively associated sequence of positive random variables with and . Denote and [gamma]=[sigma]/[mu] the coefficient of variation. Under suitable conditions, we show thatwhere , F(·) is the distribution function of the random variable , and is a standard normal random variable. This extends the earlier work on independent, positive random variables (see Khurelbaatar and Rempala [2006. A note on the almost sure limit theorem for the product of partial sums. Appl. Math. Lett. 19, 191-196]).

Keywords: Almost; sure; central; limit; theorem; Products; of; sums; Positive; (negative); association (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (8)

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