Convergence rates in the law of large numbers and new kinds of convergence of random variables

2018/05/08 by Ze-Chun Hu, Wei Sun, Hu, Ze-Chun +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1805.02803

openalex publication_date 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first study convergence rates in the law of large numbers for independent and identically distributed random variables. We obtain a strong L^p-convergence version and a strongly almost sure convergence version of the law of large numbers. Second, we investigate several new kinds of convergence of random variables and discuss their relations and properties.

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