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- Title
ASYMPTOTIC CRAMÉR TYPE DECOMPOSITION FOR WIENER AND WIGNER INTEGRALS.
- Authors
BOURGUIN, SOLESNE; BRETON, JEAN-CHRISTOPHE
- Abstract
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.
- Subjects
ASYMPTOTIC expansions; WIENER integrals; MATHEMATICAL decomposition; WIGNER distribution; GAUSSIAN distribution; RANDOM variables; FREE probability theory
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2013, Vol 16, Issue 1, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025713500057