Affiliation: | (1) Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada;(2) Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie No 13, 761 00 Bucharest 5, Romania |
Abstract: | Let X1, X2,... be, i.i.d. random variables, and put . We find necessary and sufficient moment conditions for , where δ≥ 0 and q>0, and with an>0 and bn is either or The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc |