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

Ze-Chun Hu; Wei Sun

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arXiv · 1805.02803

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

Ze-Chun Hu·Wei Sun

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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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Ze-Chun Hu, Wei Sun. 2018-05-08. Convergence rates in the law of large numbers and new kinds of convergence of random variables. https://arxiv.org/abs/1805.02803

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