Remarks on the tail order on moment sequences

Vincent Bürgin; Jeremias Epperlein; Fabian Wirth

doi:10.1016/j.jmaa.2022.126135

Remarks on the tail order on moment sequences

Vincent Bürgin, Jeremias Epperlein, Fabian Wirth

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Article number	126135
Journal	Journal of Mathematical Analysis and Applications
Volume	512
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126135
State	Published - 1 Aug 2022
Externally published	Yes

Keywords

Distribution-valued games
Moment sequences
Müntz-Szász theorem
Stochastic orders
Tail order

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2022.126135

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title = "Remarks on the tail order on moment sequences",

abstract = "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.",

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AU - Epperlein, Jeremias

AU - Wirth, Fabian

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N2 - 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.

AB - 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.

KW - Distribution-valued games

KW - Moment sequences

KW - Müntz-Szász theorem

KW - Stochastic orders

KW - Tail order

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JO - Journal of Mathematical Analysis and Applications

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ER -

Remarks on the tail order on moment sequences

Abstract

Keywords

ASJC Scopus subject areas

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