Central limit theorems for multiple stochastic integrals and Malliavin calculus

David Nualart; Salvador Ortiz

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Central limit theorems for multiple stochastic integrals and Malliavin calculus

David Nualart·Salvador Ortiz

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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 extend our result to the multidimensional case and prove a weak convergence result for a sequence of square integrable random variables.

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David Nualart, Salvador Ortiz. 2007-03-09. Central limit theorems for multiple stochastic integrals and Malliavin calculus. https://arxiv.org/abs/math/0703240

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