Geodesic
What are cumulants?
Documenta mathematica, Tome 4 (1999), pp. 601-622
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Let P be the set of all probability measures on R possessing moments of every order. Consider P as a semigroup with respect to convolution. After topologizing P in a natural way, we determine all continuous homomorphisms of P 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.
DOI : 10.4171/dm/69
Classification : 60-03, 60E05, 60E10
Mots-clés : semi-invariant, character, semigroup, convolution, additive functional, characteristic function, equivariance, expectation, halász, historical note, homomorphism, mean, moment, multiplicative functional, ruzsa, semiinvariant, székely, variance 
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     author = {Lutz Mattner},
     title = {What are cumulants?},
     journal = {Documenta mathematica},
     pages = {601--622},
     year = {1999},
     volume = {4},
     doi = {10.4171/dm/69},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/69/}
}
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Lutz Mattner. What are cumulants?. Documenta mathematica, Tome 4 (1999), pp. 601-622. doi: 10.4171/dm/69

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