Approximation to stable law by Lindeberg's method
Authors:
Preprint
Abstract
By Lindeberg's method, we develop in this paper an approximation to one dimensional (possibly) asymmetric $\alpha$-stable distributions with $\alpha \in (0,2)$ in smooth Wasserstein distance. Our main tools are Taylor-like expansion and Dynkin's formula of stable process.
Keywords
All Related Versions
This publication has 14 references indexed in Scilit:
- Stein’s Method for Asymmetric $\alpha $-stable Distributions, with Application to the Stable CLTJournal of Theoretical Probability, 2020
- On Stein's Method for Infinitely Divisible Laws with Finite First Moment2019
- Heat kernels for time-dependent non-symmetric stable-like operatorsJournal of Mathematical Analysis and Applications, 2018
- Normal Approximation by Stein’s Method2011
- Random matrices: Universality of local eigenvalue statisticsActa Mathematica, 2011
- On Two Aproaches to Approximation of Multidimensional Stable LawsJournal of Multivariate Analysis, 2002
- Rate of Convergence to a Stable LawSIAM Journal on Applied Mathematics, 2001
- Some remarks on the rate of convergence to stable lawsLithuanian Mathematical Journal, 1998
- Approximation Theory in the Central Limit Theorem1989
- Limit theorems for polylinear formsJournal of Multivariate Analysis, 1979