Central limit theorems for multiple stochastic integrals and Malliavin calculus
We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We also give a new proof of the main theorem in [D. Nualart, G. Peccati, Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33 (2005) 177-193] using techniques of Malliavin calculus. Finally, we extend our result to the multidimensional case and prove a weak convergence result for a sequence of square integrable random vectors, giving an application.
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Volume (Year): 118 (2008)
Issue (Month): 4 (April)
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- Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.