MMN-537
Almost sure convergence of weighted sums
Abstract
Let ${X, X_n, nge 1}$ be a sequence of
identically distributed random variables and ${a_{i,n}, 1le ile n}$ be a triangular array of constants. In this short paper, we establish a general almost sure convergence theorem for the weighted
sum $S_n=sum_{i=1}^n a_{i,n} X_i$. Our results improves the works of Sung [14]. Furthermore, almost sure convergence theorems of $S_n$ for negatively associated random variables, martingale difference sequence and $
ho$-mixing sequence are
obtained.
Vol. 14 (2013), No. 1, pp. 173-181
DOI: 10.18514/MMN.2013.537