Almost sure invariance principles for mixing sequences of 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 Invariance Principle for Random Piecewise Expanding Maps

The objective of this note is to prove the almost sure invariance principle (ASIP) for a large class of random dynamical systems. The random dynamics is driven by an invertiblemeasure preserving transformation σ of (Ω,F ,P) called the base transformation. Trajectories in the phase space X are formed by concatenations f ω := fσn−1ω ◦ · · · ◦ fσω ◦ fω of maps from a family of maps fω : X → X, ω ∈...

Strong Invariance Principles for Dependent Random Variables

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...

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

THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.