Complete Moment Convergence for Sung’s Type Weighted Sums of B-Valued Random Elements

Abstract

Let p≥1/α and 1/2p. We give necessary and sufficient conditions for complete moment convergence of the form ∑n=1∞n(p-v)α-2E∑i=1naniXi-εnα+v0, where 0<v<p. A strong law of large numbers for weighted sums of independent B-valued random elements is also obtained.