Note on an intermediate Baum-Katz theorems under sub-linear expectations

2025/08/26 by Mingzhou, Xu, Jinjin, Yang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.18878

Abstract

We study the Hsu-Robbins-Erdös theorem to the case when all moments under sub-linear expectations exist, but the moment generating function does not, viz, we suppose that C_\mathbbv\exp\(log⁺|X|)^α\\<∞ for some α>1. We also investigate multi-index version.

Citations

• Equivalent conditions of complete convergence for weighted sums of sequences of i. i. d. random variables under sublinear expectations
• Three series theorem for independent random variables under sub-linear expectations with applications
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type

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• Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields
• Normal Approximation by Stein's Method under Sublinear Expectations
• Convergence of series of conditional expectations
• Baum-Katz type theorems with exact threshold