Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2009

Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields

Giovanni Peccati
  • Function : Author
  • PersonId : 829856

Abstract

We show how to detect optimal Berry-Esséen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and the method of moments and cumulants, and provide de facto local (one term) Edgeworth expansions. The findings of the present paper represent a further refinement of the main results proved in Nourdin and Peccati (2009b). Among several examples, we discuss three crucial applications: (i) to Toeplitz quadratic functionals of continuous-time stationary processes (extending results by Ginovyan (1994) and Ginovyan and Sahakyan (2007)), (ii) to ``exploding'' quadratic functionals of a Brownian sheet, and (iii) to a continuous-time version of the Breuer-Major CLT for functionals of a fractional Brownian motion.
Fichier principal
Vignette du fichier
Steinlocal-final-aop.pdf (305.63 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00260597 , version 1 (04-03-2008)
hal-00260597 , version 2 (30-01-2009)

Identifiers

Cite

Ivan Nourdin, Giovanni Peccati. Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields. 2009. ⟨hal-00260597v2⟩
108 View
231 Download

Altmetric

Share

Gmail Facebook X LinkedIn More