On the characterization of certain similarly ordered super-additive functionals
Author:
Heinz J. Skala
Journal:
Proc. Amer. Math. Soc. 126 (1998), 1349-1353
MSC (1991):
Primary 28C05; Secondary 47H07, 60A05, 90A05
DOI:
https://doi.org/10.1090/S0002-9939-98-04702-9
MathSciNet review:
1476392
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Functionals which behave (sub-, super-) additively on similarly ordered functions occur quite naturally in many contexts. In the present paper we characterize (super-) additive functionals which are defined on a family of functions with the Stone-property in terms of their naturally adjoined dyadic martingales. As corollaries we obtain essential generalizations of integral representations as derived by Schmeidler (1986) and discussed in a recent monograph of Denneberg (1994).
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Additional Information
Heinz J. Skala
Affiliation:
Department of Statistics, University of Paderborn, Warburgerstrasse 100, 33095 Paderborn, Germany
Keywords:
Similarly ordered,
comonotonic,
integral representation,
martingales
Received by editor(s):
August 29, 1996
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1998
American Mathematical Society
