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2018•arXiv (Cornell University)Open access

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

Ze-Chun Hu, Wei Sun

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Abstract

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

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What this paper is about

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

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Available abstract

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

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

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