Central limit theorems for multiple stochastic integrals and Malliavin calculus |
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Authors: | D Nualart S Ortiz-Latorre |
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Institution: | 1. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045, USA;2. Departament de Probabilitat, Lògica i Estadística, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain |
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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. |
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Keywords: | 60F05 60G15 60H05 60H07 |
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