Almost sure central limit theorems for m-dependent random variables

Central Limit Theorems for Dependent Random Variables

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...

Almost Sure Central Limit Theorems for Strongly Mixing and Associated Random Variables

The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables

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...

Almost sure local limit theorems

Chung and Erdös (1951) are among the first to prove some form of an almost sure local limit theorem (cf. Csáki et al., 1993). Here we propose a formulation of such statements and discuss related problems. Surely, Frits will enjoy them. c ©2001, June 19.

Central and Local Limit Theories in Markov Dependent Random Variables