ON ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LNQD RANDOM VARIABLES

Jeong-Yeol Choi, So-Youn Kim, Jong-Il Baek
2012 Honam Mathematical Journal  
Let {Xni, 1 ≤ i ≤ n, n ≥ 1} be a sequence of LN QD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums n i=1 aniXni for LN QD by using a new exponential inequality, where {ani, 1 ≤ i ≤ n, n ≥ 1} is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LN QD case.
doi:10.5831/hmj.2012.34.2.241 fatcat:gs4hkwyhd5g4zotyae7jwx22du