Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156209 | Stochastic Processes and their Applications | 2008 | 15 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
D. Nualart, S. Ortiz-Latorre,