What are cumulants?

  • Lutz Mattner

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Let \cP\cP be the set of all probability measures on R\R possessing moments of every order. Consider \cP\cP as a semigroup with respect to convolution. After topologizing \cP\cP in a natural way, we determine all continuous homomorphisms of \cP\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 ii and exponentiation.

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Lutz Mattner, What are cumulants?. Doc. Math. 4 (1999), pp. 601–622

DOI 10.4171/DM/69