Central limit theorems for multiple stochastic integrals and Malliavin calculus

D. Nualart and S. Ortiz-Latorre

Stochastic Processes and their Applications, 2008, vol. 118, issue 4, 614-628

Abstract: 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.

Keywords: Multiple; stochastic; integrals; Limit; theorems; Gaussian; processes; Malliavin; calculus; Weak; convergence (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (25)

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