Let be a stationary sequence of pair wise negative quadrant dependent random variables with survival function {,1}nXn?F(x)=P[X>x]. The empirical survival function ()nFx based on 12,,...,nXXX is proposed as an estimator for ()nFx. Strong consistency and point wise as well as uniform of ()nFx are discussed

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

We consider the many-body time evolution of weakly interacting bosons in mean field regime for initial coherent states. show that bounded k-particle operators, corresponding to dependent random variables, satisfy both, a law large numbers and central limit theorem.

in this paper, we generalize a theorem of shao [12] by assuming that 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 -th absolute moment the weighted sums converge to zero as where and is an array of real numbe...

We discuss sufficient conditions that guarantee the existence of asymptotic expansions for Central Limit Theorem weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. primarily use spectral techniques to obtain results.