Minimal Lp-densities with prescribed marginals

Paolo Guasoni; Eberhard Mayerhofer; Mingchuan Zhao

doi:10.3150/20-BEJ1250

Minimal L^p-densities with prescribed marginals

Paolo Guasoni, Eberhard Mayerhofer, Mingchuan Zhao

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

Abstract

We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.

Original language	English
Pages (from-to)	576-585
Number of pages	10
Journal	Bernoulli
Volume	27
Issue number	1
DOIs	https://doi.org/10.3150/20-BEJ1250
Publication status	Published - Feb 2021

Keywords

Banach spaces
Integral equations
Multivariate distributions
Sharp estimates

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10.3150/20-BEJ1250

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abstract = "We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.",

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author = "Paolo Guasoni and Eberhard Mayerhofer and Mingchuan Zhao",

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AU - Mayerhofer, Eberhard

AU - Zhao, Mingchuan

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N2 - We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.

AB - We derive sharp lower bounds for Lp-functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.

KW - Banach spaces

KW - Integral equations

KW - Multivariate distributions

KW - Sharp estimates

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VL - 27

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JO - Bernoulli

JF - Bernoulli

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Minimal L^p-densities with prescribed marginals

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Keywords

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