Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws

Masaru Shintani and Ken Umeno

Papers from arXiv.org

Abstract: In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical stochastic processes with power-laws converges in density to a unique stable distribution. This property can be used to explain the universality of stable laws such that the sums of the logarithmic return of non-identical stock price fluctuations follow stable distributions.

Date: 2017-02, Revised 2017-08
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1702.02826

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