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

Access to Document

10.3150/20-BEJ1250

Cite this

@article{21e35bcc877b4e14af4d83cd04e701bc,

title = "Minimal Lp-densities with prescribed marginals",

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.",

keywords = "Banach spaces, Integral equations, Multivariate distributions, Sharp estimates",

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

note = "Publisher Copyright: {\textcopyright} 2021 ISI/BS.",

year = "2021",

month = feb,

doi = "10.3150/20-BEJ1250",

language = "English",

volume = "27",

pages = "576--585",

journal = "Bernoulli",

issn = "1350-7265",

number = "1",

}

TY - JOUR

T1 - Minimal Lp-densities with prescribed marginals

AU - Guasoni, Paolo

AU - Mayerhofer, Eberhard

AU - Zhao, Mingchuan

PY - 2021/2

Y1 - 2021/2

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

UR - https://www.scopus.com/pages/publications/85097465396

U2 - 10.3150/20-BEJ1250

DO - 10.3150/20-BEJ1250

M3 - Article

AN - SCOPUS:85097465396

SN - 1350-7265

VL - 27

SP - 576

EP - 585

JO - Bernoulli

JF - Bernoulli

IS - 1

ER -

Minimal L^p-densities with prescribed marginals

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this