Heyde’s theorem under the sub-linear expectations

Li-Xin Zhang

Statistics & Probability Letters, 2021, vol. 170, issue C

Abstract: Let {Xn;n≥1} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω,ℋ,E) with a capacity V generated by E. The convergence rate of ∑n=1∞V(|∑k=1nXk|>ϵn) as ϵ→0 is studied. Heyde (1975)’s theorem is shown under the sub-linear expectation.

Keywords: Sub-linear expectation; Law of large numbers; Complete convergence; Precise asymptotics (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.108987

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