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Multivariate Stable Approximation by Stein’s Method

Author

Listed:
  • Peng Chen

    (Nanjing University of Aeronautics and Astronautics)

  • Ivan Nourdin

    (Université du Luxembourg)

  • Lihu Xu

    (University of Macau
    Zhuhai UM Science & Technology Research Institute)

  • Xiaochuan Yang

    (Brunel University)

Abstract

By a delicate analysis for the Stein’s equation associated with the $$\alpha $$ α -stable law approximation with $$\alpha \in (0,2)$$ α ∈ ( 0 , 2 ) , we prove a quantitative stable central limit theorem in Wasserstein-type distance, which generalizes the results in the series of work (Chen et al. in J Theor Probab 34(3):1382–1407, 2021; Chen et al. in J Theor Probab 35(2):1137–1186 2022; Xu in Ann Appl Probab 29(1):458–504, 2019) from the univariate case to the multiple variate case. From an explicit computation for Pareto’s distribution, we see that the rate of our approximation is sharp. The analysis of the Stein’s equation is new and has independent interest.

Suggested Citation

  • Peng Chen & Ivan Nourdin & Lihu Xu & Xiaochuan Yang, 2024. "Multivariate Stable Approximation by Stein’s Method," Journal of Theoretical Probability, Springer, vol. 37(1), pages 446-488, March.
  • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01244-x
    DOI: 10.1007/s10959-023-01244-x
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