MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let {}ijX be a double sequence of pairwise negatively dependent random variables. If P{Xij≥t}≤P{X≥t for all non-negative real numbers t and EX+X<∞plog, for 1 < p < 2, then we prove that ()()→∨→∞ΣΣ−==aeasmnmnXEXpminjijij0..1/11 (1). In addition, it also converges to 0 in. The results can be generalized to an r-dimensional array of random variables under condition L1()<∞+−1logprEXX, thus, extending Choi and Sung’s result [7] of one dimensional case for negatively dependent random variables.