Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces

2018/04/26 by Weihuan Huang, Huang, Weihuan, Panyu Wu +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1804.09971

openalex publication_date 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure central limit theorem under sub-linear expectations in this paper, which is a quasi sure convergence version of Peng's central limit theorem. Moreover, this result is a natural extension of the classical almost sure central limit theorem to the case where the probability is no longer additive. Meanwhile, we prove a new kind of strong law of large numbers for non-additive probabilities without the independent identically distributed assumption.

Citations

• A note on the almost sure central limit theorem
• A strong law of large numbers for non-additive probabilities

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