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Central limit theorems for multiple stochastic integrals and Malliavin calculus

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David Nualart, Salvador Ortiz

Probability · Submitted 8 Mar 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDmath/0703240 (version 2)
Pith IDXYH4VIOH, Pith's permanent record of this paper and its review
CitationDavid Nualart, Salvador Ortiz. "Central limit theorems for multiple stochastic integrals and Malliavin calculus." arXiv:math/0703240 (2007). https://pith.science/paper/XYH4VIOH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,302 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 0.69 0.95 0.77 asserted 1.00
s1 We extend our result to the multidimensional case and prove a weak convergence result for a sequence of square integrable random variables. contribution 0.72 0.94 0.17 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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