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Article Dans Une Revue Infinite Dimensional Analysis, Quantum Probability and Related Topics Année : 2013

Asymptotic Cramér type decomposition for Wiener and Wigner integrals

Résumé

We investigate generalizations of the Cramér theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are Gaussian. We prove asymptotic counterparts of such decomposition results for multiple Wiener integrals and prove that similar results are true for the (asymptotic) decomposition of the semicircular distribution into free multiple Wigner integrals.
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Dates et versions

hal-00731849 , version 1 (13-09-2012)

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Solesne Bourguin, Jean-Christophe Breton. Asymptotic Cramér type decomposition for Wiener and Wigner integrals. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2013, 16 (1), ⟨10.1142/S0219025713500057⟩. ⟨hal-00731849⟩
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