The Annals of Probability

Central limit theorems for sequences of multiple stochastic integrals

David Nualart and Giovanni Peccati

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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.

Article information

Source
Ann. Probab., Volume 33, Number 1 (2005), 177-193.

Dates
First available in Project Euclid: 11 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1108141724

Digital Object Identifier
doi:10.1214/009117904000000621

Mathematical Reviews number (MathSciNet)
MR2118863

Zentralblatt MATH identifier
1097.60007

Subjects
Primary: 60F05: Central limit and other weak theorems 60H05: Stochastic integrals

Keywords
Multiple stochastic integrals Brownian motion weak convergence fractional Brownian motion Brownian sheet

Citation

Nualart, David; Peccati, Giovanni. Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 (2005), no. 1, 177--193. doi:10.1214/009117904000000621. https://projecteuclid.org/euclid.aop/1108141724


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