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arXiv · 1702.02826

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

Masaru Shintani·Ken Umeno
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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.

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Masaru Shintani, Ken Umeno. 2017-02-09. Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws. https://doi.org/10.7566/jpsj.87.043003

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