Precise asymptotics for maxima of partial sums under sub-linear expectation

Xue Ding and Yong Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5284-5296

Abstract: Let {X,Xn,n≥1} be a sequence of independent and identically distributed random variables in a sub-linear expectation (Ω,H,Ê) with a capacity 𝕍 under Ê. In this article, under some suitable conditions, two general forms of precise asymptotics for maxima of partial sums hold under sub-linear expectation. It can describe the relations among the boundary function, weighted function, convergence rate, and limit value in studies of precise asymptotics. The results extend some precise asymptotics from the traditional probability space to the sub-linear expectation space, and also extend the precise asymptotics from partial sums to maxima of partial sums.

Date: 2025
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DOI: 10.1080/03610926.2024.2435585

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