On the (p,q)-type Strong Law of Large Numbers for Sequences of Independent Random Variables

2020/08/04 by Lê Vǎn Thành, Thành, Lê Vǎn
Decision Sciences · Mathematics · #60F15 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2008.01306

openalex publication_date 2020/08/04 · openalex created_date 2020/08/10 · openalex updated_date 2026/07/28

Abstract

Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 2016) introduced a refinement of the Marcinkiewicz--Zygmund strong law of large numbers (SLLN), so-called the (p,q)-type SLLN, where 00. They obtained sets of necessary and sufficient conditions for this new type SLLN for two cases: 0p, and 1≤ p<2,q≥ 1. This paper gives a complete solution to open problems raised by Li, Qi, and Rosalsky by providing the necessary and sufficient conditions for the (p,q)-type SLLN for the cases where 0

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