Stein's method and normal approximation of poisson functionals

G. Peccati, J. L. Solé, F. Utzet, M. S. Taqqu

Research output: Contribution to journalArticleResearchpeer-review

68 Citations (Scopus)

Abstract

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esséen bounds in Central limit theorems (CLTs) involving multipleWiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.
Original languageEnglish
Pages (from-to)443-478
JournalAnnals of Probability
Volume38
Issue number2
DOIs
Publication statusPublished - 1 Mar 2010

Keywords

  • Malliavin calculus
  • Normal approximation
  • Ornstein-uhlenbeck process
  • Poisson measure
  • Stein's method
  • Wasserstein distance.

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