The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).

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.

Используя подход Н. Этемади (1981 г.) к усиленному закону больших чисел (УЗБЧ) и развитие этого подхода, предпринятое в работе Ш. Чeргe, К. Тандори В. Тотика (1983 г.), мы приводим более слабые условия, при которых УЗБЧ все еще справедлив, для попарно некоррелированных (а также "почти некоррелированных") случайных величин. Мы сосредоточиваем внимание, частности, на величинах, не являющихся один...

In the present paper, we will investigate weak laws of large numbers for weighted pairwise NQD random variables with infinite mean. The almost sure upper and lower bounds for a particular normalized weighted sum of pairwise NQD nonnegative random variables are established also.

Let {Xn, n ≥ 1} be a sequence of pairwise NQD random variables. Some complete convergences and strong laws of large numbers for a weighted sums sequence of pairwise NQD random variables are obtained. The results obtainted generalize the results of Cabrera and Volodin (see [3]).