Remarks on the tail order on moment sequences

Autor: Jeremias Epperlein, Fabian Wirth, Vincent Bürgin
Rok vydání: 2022
Předmět:
Zdroj: Journal of Mathematical Analysis and Applications. 512:126135
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2022.126135
Popis: We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified on which the order is total, but it is shown that already for the set of distributions with compactly supported smooth densities the order is not total. In particular we construct a pair of measures with smooth density for which infinitely many moments agree and another one for which the moments alternate infinitely often. This disproves some recently published claims to the contrary. Some consequences for games with distributional payoffs are discussed.
22 pages, minor changes in [v3]: consistently use natural numbers starting at 0, slightly changed Remark 19 and formulation of Theorem 10
Databáze: OpenAIRE
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