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