The moments of the maximum of normalized partial sums related to laws of the iterated logarithm under the sub-linear expectation

2022/02/25 by Zhang Li, Zhang, Li-Xin
Decision Sciences · Mathematics · #60F05 #60F15 #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2202.12583

openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \X_n;n≥ 1\ be a sequence of independent and identically distributed random variables on a sub-linear expectation space (Ω,\mathscrH,\widehat\mathbb E), S_n=X₁+…+X_n. We consider the moments of max_{n≥ 1}|S_n|/√(2nloglog n). The sufficient and necessary conditions for the moments to be finite are given. As an application, we obtain the law of the iterated logarithm for moving average processes of independent and identically distributed random variables.

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