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February 2021 Minimal $\mathcal{L}^{p}$-densities with prescribed marginals
Paolo Guasoni, Eberhard Mayerhofer, Mingchuan Zhao
Bernoulli 27(1): 576-585 (February 2021). DOI: 10.3150/20-BEJ1250

Abstract

We derive sharp lower bounds for $\mathcal{L}^{p}$-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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Paolo Guasoni. Eberhard Mayerhofer. Mingchuan Zhao. "Minimal $\mathcal{L}^{p}$-densities with prescribed marginals." Bernoulli 27 (1) 576 - 585, February 2021. https://doi.org/10.3150/20-BEJ1250

Information

Received: 1 April 2020; Revised: 1 July 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282862
MathSciNet: MR4177381
Digital Object Identifier: 10.3150/20-BEJ1250

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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