scholarly journals ASYMPTOTIC CRAMÉR TYPE DECOMPOSITION FOR WIENER AND WIGNER INTEGRALS

2013 ◽  
Vol 16 (01) ◽  
pp. 1350005
Author(s):  
SOLESNE BOURGUIN ◽  
JEAN-CHRISTOPHE BRETON
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Gaussian Random Variable ◽  
Independent Random Variables ◽  
Asymptotic Decomposition ◽  
Type Decomposition

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.

Asymptotic decomposition of slow integral manifolds

1994 ◽  
Vol 35 (6) ◽  
pp. 1119-1132 ◽  
Author(s):  
L. I. Kononenko ◽  
V. A. Sobolev
Keyword(s):  
Asymptotic Decomposition ◽  
Integral Manifolds
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