On complete convergence and strong law for weighted sums of i.i.d. random variables (Q1722443)

Summary: We improve and generalize the result of \textit{W. F. Stout} [Almost sure convergence. New York, NY: Academic Press (1974; Zbl 0321.60022), Theorem 4.1.3]. In particular, the sharp moment conditions are obtained and some well-known results can be obtained as special cases of the main result. The method of the proof is completely different from that in [loc. cit.]. We also improve and generalize [\textit{D. Li} et al., J. Theor. Probab. 8, No. 1, 49--76 (1995; Zbl 0814.60026)] strong law for weighted sums of i.i.d.\ random variables.