Cumulants and moments
type: Item
instance of: scholarly article
title: Cumulants and moments
zbMATH Open document ID: 0545.47028
DOI: 10.1016/0034-4877(80)90040-3
author: Walter Wyss
published in: Reports on Mathematical Physics
publication date: 1980-01-01T00:00:00Z
review text: In [Lett. Math. Phys. 2, 207-217 (1978; Zbl 0379.16018)] the concept of quasi-multiplication on rings and algebras was introduced. In the present paper the author looks at a \({}^*\)-algebra of terminating sequences whose entries are complex numbers. The set of normalized linear functions on this algebra is then equipped with a quasi-multiplication and also with a multiplication. The two operations are intimately related, but both have their own right. This is shown for sequences of moments (positive linear functionals, states) and their corresponding sequences of cumulants. Necessary and sufficient conditions for a sequence to be a sequence of moments, and a sequence to be a sequence of cumulants, are also given. Further studies, not mentioned in this paper, include higher derivatives of composite functions (Faà di Bruno), the construction of new sequences of moments from given sequences of moments, and the statement, that every sequence of moments is a sequence of cumulants.
Mathematics Subject Classification ID: 47L90
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 16Y60
zbMATH DE Number: 3868068
zbMATH Keywords: quasi-multiplication on rings and algebras
zbMATH Keywords: \({}^*\)-algebra of terminating sequences
zbMATH Keywords: normalized linear functions
zbMATH Keywords: sequences of moments
zbMATH Keywords: states
zbMATH Keywords: sequence of moments
zbMATH Keywords: sequence of cumulants
MaRDI profile type: Publication
full work available at URL: 0034-4877(80)90040-3
OpenAlex ID: W2032060025
cites work: The quasi-multiplication on rings and algebras
cites work: Q5727877
description: scientific article; zbMATH DE number 3868068