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Peng Chen - One of the best experts on this subject based on the ideXlab platform.

  • Approximation to stable law by the Lindeberg principle
    Journal of Mathematical Analysis and Applications, 2019
    Co-Authors: Peng Chen
    Abstract:

    Abstract 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.

  • approximation to the stable law by Lindeberg principle
    arXiv: Probability, 2018
    Co-Authors: Peng Chen
    Abstract:

    By the Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric $\alpha$-stable distributions with $\alpha \in (0,2)$ 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 $\alpha \in (0,1]$ is proved by a new method other than Fourier analysis. Our main tools are a Taylor-like expansion and a Kolmogorov forward equation.

  • Approximation to the stable law by Lindeberg principle
    arXiv: Probability, 2018
    Co-Authors: Peng Chen
    Abstract:

    By Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric $\alpha$-stable distributions with $\alpha \in (0,2)$ in smooth Wasserstein distance, which implies the stable central limit theorem. Our main tools are Taylor-like expansion and Dynkin's formula of stable process.