The Annals of Probability

Central limit theorems for sequences of multiple stochastic integrals

David Nualart and Giovanni Peccati

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

First available in Project Euclid: 11 February 2005

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Zentralblatt MATH identifier

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

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


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.

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