On Convergence in $r$-Mean of Normalized Partial Sums

on direct sums of baer modules

the notion of baer modules was defined recently

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums

Let {X,Xn}n∈N be a sequence of independent and identically distributed i.i.d. positive random variables with a nondegenerate distribution function and EX μ > 0. For each n ≥ 1, the symbol Sn/Vn denotes self-normalized partial sums, where Sn ∑n i 1 Xi and V 2 n ∑n i 1 Xi − μ . We say that the random variable X belongs to the domain of attraction of the normal law if there exist constants an > 0,...

Convergence Theorems for Partial Sums of Arbitrary Stochastic Sequences

On the Complete Convergence ofWeighted Sums for Dependent Random Variables

We study the limiting behavior of weighted sums for negatively associated (NA) random variables. We extend results in Wu (1999) and a theorem in Chow and Lai (1973) for NA random variables.