Limit Theorems For Product Sums Of Negatively Dependent Random Variables

SummaryBy turning the product sums to the product of partial sums, this paper discuss the strong law of large numbers and the law of the iterated logarithm for product sums of NA sequences, extend and improve the Brunk-Chung strong law of large numbers, Kolmogorov strong law of large numbers, Marcinkiewicz strong law of large numbers, the corresponding results in Petrov(1975, Ch9)?81 and Wittmann (1 985)t27], the Kolmogorov law of the iterated logarithm and the Hartman-Winter law of the iterated logarithm; in chap 4, we study the strong stability for Stout type weighted product sums and the Marcinkiewicz strong law of large numbers for another type weighted product sums of NA sequences, extend and improve the corresponding results in Bai & Cheng(2000)1211 at last, in chap 5 and 6, we discuss the Marcinkiewicz strong law of large numbers and the strong stability for Jamison type weighted product sums of pairwise NQD sequences and pairwise PQD sequences, extend and improve the corresponding results in Etemadi (1983)[23] and Birkel (1989). Though, pairwise PQD random variables are not belonging to negatively dependent random variables, the core of this paper are still to be the following two kinds negatively dependent random variables: NA and pairwise NQD.Jigao Yan(Probability theory and Mathematical Statistics)Directed by Professor Yuebao Wang...