In a celebrated work by Shao [13] several inequalities for negatively ASSOCIATED RANDOM variables were proved. In this paper we obtain some maximal inequalities for ASSOCIATED RANDOM variables. Also we establish a maximal inequality for DEMIMARTINGALES which generalizes and improves the result of Christofides [4].

We study the limiting behavior of weighted sums for negatively ASSOCIATED (NA) RANDOM variables. We extend results in Wu (1999) and a theorem in Chow and Lai (1973) for NA RANDOM variables.

Let {X}n be a sequence of arbitrary RANDOM variables with EXn=0 and EX2n<¥, for every n³1 and {a nk} be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of RANDOM variables and also, we will prove COMPLETE convergence for weighted sums S nj=1(anjXj), under some conditions on anj and sequence {Xn, n³1}.

In this paper, the properties of fuzzy RANDOM variables with new meter and some extended results of monotone convergence theorem and dominated convergence theorem for fuzzy RANDOM variables are discussed. The main result is given by usingDp, q -distance defined on the set of fuzzy numbers.

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) RANDOM variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. RANDOM variables is extended in NOD setting by generalized Gaussian techniques.  

In this paper, we generalize a theorem of Shao [12] by assuming that {Xn} is a sequence of linear negatively dependent RANDOM variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically RANDOM variables with finite p –th absolute moment (p³2) p the weighted sums 1/An åni=1 aniXi converge to zero as where An=n1/p and (åni=1 a2ni) {an,i} a is an array of real numbers. Moreover, we prove the almost sure convergence for weighted sums åni=1 aniX, n³1, when {Xi, i ³ 1} i is a sequence of pairwise negative quadrant dependence stochastically bounded RANDOM variables under some suitable conditions on an,i.

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent RANDOM variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.    

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent RANDOM variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.