Approximation to stable law by the Lindeberg principle
Journal of Mathematical Analysis and Applications(2019)
摘要
By the Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric α-stable distributions with α∈(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 α∈(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.
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关键词
Asymmetric α-stable distribution,The Lindeberg principle,A Kolmogorov forward equation,Stable central limit theorem
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