Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws
Statistics Theory
2018-04-18 v6 Mathematical Physics
math.MP
Economics
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1702.02826,
title = {Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws},
author = {Masaru Shintani and Ken Umeno},
journal= {arXiv preprint arXiv:1702.02826},
year = {2018}
}
Comments
4pages,1figure