Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The optimal fourth moment theorem
HTML articles powered by AMS MathViewer

by Ivan Nourdin and Giovanni Peccati PDF
Proc. Amer. Math. Soc. 143 (2015), 3123-3133 Request permission

Abstract:

We compute the exact rates of convergence in total variation associated with the ‘fourth moment theorem’ by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 60F05, 60G15, 60H07
  • Retrieve articles in all journals with MSC (2010): 60F05, 60G15, 60H07
Additional Information
  • Ivan Nourdin
  • Affiliation: Université du Luxembourg. Faculté des Sciences, de la Technologie et de la Communication; UR en Mathématiques. 6, Rui Richard Coudenhove-Kalergi, L-1359 Luxembourg
  • MR Author ID: 730973
  • Giovanni Peccati
  • Affiliation: Université du Luxembourg. Faculté des Sciences, de la Technologie et de la Communication; UR en Mathématiques. 6, Rui Richard Coudenhove-Kalergi, L-1359 Luxembourg
  • MR Author ID: 683104
  • Received by editor(s): May 7, 2013
  • Received by editor(s) in revised form: October 11, 2013
  • Published electronically: March 18, 2015
  • Additional Notes: The first author was partially supported by the (French) ANR grant ‘Malliavin, Stein and Stochastic Equations with Irregular Coefficients’ [ANR-10-BLAN-0121]
    The second author was partially supported by the grant F1R-MTH-PUL-12PAMP from the University of Luxembourg
  • Communicated by: Mark M. Meerschaert
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3123-3133
  • MSC (2010): Primary 60F05, 60G15, 60H07
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12417-3
  • MathSciNet review: 3336636