On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

Abstract

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

“…For (i), similar to the proof of Lemma 3 in [9] and assuming x (1/p) � y, then ( 16) is obtained. For (ii), similar to the proof eorem 6 in [20], we can get, for any a > 1, ( 18) is satisfied.…”