Approximation to stable law by the Lindeberg principle

[摘要] By the Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric alpha-stable distributions with alpha is an element of (0, 2) in the smooth Wasserstein distance. It is the first time that the general stable central limit theorem is proved by the Lindeberg principle, and that this theorem with alpha is an element of (0, 1] is proved by a new method other than Fourier analysis. Our main tools are a Taylor-like expansion and a Kolmogorov forward equation. (C) 2019 Published by Elsevier Inc.

[发布日期] 2019-12-15

[关键词] Asymmetric alpha-stable distribution;The Lindeberg principle;A Kolmogorov forward equation;Stable central limit theorem