Central limit theorems for sequences of multiple stochastic integrals

2005/03/25 by David Nualart, Giovanni Peccati · 6 citations
Mathematics · #math.PR #msc:60F05 #msc:60H05.

paper · pdf · doi:10.1214/009117904000000621

published as Annals of Probability 2005, Vol. 33, No. 1, 177-193 · Published at http://dx.doi.org/10.1214/009117904000000621 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2005/03/25 · arxiv updated 2009/12/01

Abstract

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes.

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