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2018•arXiv (Cornell University)Open access

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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What this paper is about

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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Available 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.

Key concepts: Independent and identically distributed random variables, Law of large numbers, Convergence (economics), Convergence of random variables, Proofs of convergence of random variables, Mathematics, Random variable, Convergence tests

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