Two Convergence Theorems of Weighted Sums of Random Variables

Abstract:

      In the note we present two theorems on convergence of weighted sums of random variables. The relative extensions to random elements in a separable normed linear space are also discussed.Theorem 1 and Corollary 1 are extensions of the theorems of Chow and Lai, Padgett and Taylor, Bozognia and Bhaskara Rao, and Wei and Taylor. Theorem 2 is an extension of another result of Chow and Lai.