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 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.

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions. 1. Introduction. Strong laws of large numbers (SLLN), laws of the iterated logarithm (LIL), centr...

Let {Xn, n ≥ 1} be a sequence of independent and identically random variables. In 1947 Hsu and Rabbins proved that if E[X] = 0 and E[X2] < ∞, then 1 n ∑n k=1Xk converges to 0 completely. Recently, the strong convergence of weighted sums for the case of independent random variables has been discussed by Wu (1999), Hu and et. (2000, 2003) proved the complete convergence theorem for arrays of inde...

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample path properties of empirical distribution functions are also discussed. The results are applied to linear processes and Markov chains.

1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...