Bernoulli

  • Bernoulli
  • Volume 20, Number 2 (2014), 697-715.

Universal Gaussian fluctuations on the discrete Poisson chaos

Giovanni Peccati and Cengbo Zheng

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Abstract

We prove that homogeneous sums inside a fixed discrete Poisson chaos are universal with respect to normal approximations. This result parallels some recent findings, in a Gaussian context, by Nourdin, Peccati and Reinert (Ann. Probab. 38 (2010) 1947–1985). As a by-product of our analysis, we provide some refinements of the CLTs for random variables on the Poisson space proved by Peccati, Solé, Taqqu and Utzet (Ann. Probab. 38 (2010) 443–478) and by Peccati and Zheng (Electron. J. Probab. 15 (2010) 1487–1527).

Article information

Source
Bernoulli, Volume 20, Number 2 (2014), 697-715.

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393594003

Digital Object Identifier
doi:10.3150/12-BEJ503

Mathematical Reviews number (MathSciNet)
MR3178515

Zentralblatt MATH identifier
1302.60059

Keywords
Central Limit Theorems contractions discrete Poisson chaos universality

Citation

Peccati, Giovanni; Zheng, Cengbo. Universal Gaussian fluctuations on the discrete Poisson chaos. Bernoulli 20 (2014), no. 2, 697--715. doi:10.3150/12-BEJ503. https://projecteuclid.org/euclid.bj/1393594003


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