Geodesic
What are cumulants?
Documenta mathematica, Tome 4 (1999), pp. 601-622.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $\cP$ be the set of all probability measures on $\R$ possessing moments of every order. Consider $\cP$ as a semigroup with respect to convolution. After topologizing $\cP$ in a natural way, we determine all continuous homomorphisms of $\cP$ into the unit circle and, as a corollary, those into the real line. The latter are precisely the finite linear combinations of cumulants, and from these all the former are obtained via multiplication by $i$ and exponentiation.
Classification : 60E05, 60E10, 60-03
Keywords: additive functional, characteristic function, character, convolution, equivariance, expectation, halász, historical note, homomorphism, mean, moment, multiplicative functional, ruzsa, semi-invariant, semiinvariant, semigroup, székely, variance 
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     language = {en},
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Mattner, Lutz. What are cumulants?. Documenta mathematica, Tome 4 (1999), pp. 601-622. http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a2/