Acta Mathematica Academiae Scientiarum Hungaricae 65. (1994)

1994 / 1. szám - Móricz F. - Su, Kuo-Liang - Taylor, R. L.: Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces

Acta Math. Hangar. 65 (1) (1994), 1-16. STRONG LAWS OF LARGE NUMBERS FOR ARRAYS OF ORTHOGONAL RANDOM ELEMENTS IN BANACH SPACES F. MÓRICZ (Szeged), KUO-LIANG SU (Taichung) and R. L. TAYLOR (Athens) Introduction Several previous authors have investigated laws of large numbers for arrays of orthogonal Banach space-valued random elements. The general goal is to obtain conditions which yield the convergence provided that E E ['°й(; + 1)1 ” [lo&ü + 1,] p < 00. i=1 j-1 J where {Xij} is an array of orthogonal Banach space-valued random elements with zero means and EWXijW* < oo, 1 ^ p ^ 2 for all i,j ^ 1. Móricz [2] defined quasi-orthogonality for an array of random variables { Xik } 3.S I E(XikXjt\ üp{\i~ il,\k - /|) {EXl)ll\EXlf\ where p(m,n) is a double sequence such that 0236-5294/94/$ 4.00 © 1994 Akadémiai Kiadó, Budapest m n E E xn 0 as min(m, n) -> oo or max(m,n) —► oo 1 manp OO OO Y Yp^m'n^ < 00•

Next