Weak laws of large numbers for weighted sums of arrays of random variables under sublinear expectation

Cheng Hu, Li Wang and Tongxing Li

Communications in Statistics - Theory and Methods, 2024, vol. 54, issue 12, 3711-3731

Abstract: In this article, we introduce a new concept of integrability called extended residually h-integrability with exponent r, which deals with weighted sums of arrays under sublinear expectation. The classical copy of this concept extends the residually h-integrability given by Wang, Hu, and Volodin (2018). On this basis, we obtain three forms of weak laws of large numbers for weighted sums of arrays of rowwise negatively dependent or rowwise independent random variables, respectively, under sublinear expectation. As corollaries, we get some weak laws of large numbers for arrays of random variables with normalizing factor kn under sublinear expectation.

Date: 2024
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DOI: 10.1080/03610926.2024.2403545

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