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Central limit theorems for sequences of multiple stochastic integrals

Nualart, David
; 
Peccati, Giovanni
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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.
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This is the published version, also available here: http://dx.doi.org/10.1214/009117904000000621.
Date
2005-01-01
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Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_AP_33(1)177.pdf
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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. http://dx.doi.org/10.1214/009117904000000621.
URI
https://hdl.handle.net/1808/17028
DOI
10.1214/009117904000000621
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