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

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  • Masaru Shintani
  • Ken Umeno

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.

Suggested Citation

  • Masaru Shintani & Ken Umeno, 2017. "Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws," Papers 1702.02826, arXiv.org, revised Aug 2017.
  • Handle: RePEc:arx:papers:1702.02826
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    File URL: http://arxiv.org/pdf/1702.02826
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