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Journal of Convex Analysis 23 (2016), No. 4, 1125--1136
Copyright Heldermann Verlag 2016

Quantiles and Convexity

Michel Valadier
IMAG, Université Montpellier II, Place Eugène Bataillon, Case Courier 051, 34095 Montpellier Cedex, France

A real random variable admits median(s) and quantiles. These values minimize convex functions on the reals R. This is known. We discuss these results and their relationship with some notions about functions of bounded variation developed by J. J. Moreau in his mathematical work in view of the mechanical phenomena which are shocks and friction, especially filled-in graphs and Stieltjes measures of products of BV functions.

Keywords: Median, quantile, convexity, subdifferential, monotone operator, minimizer, BV function.

MSC: 62E99, 52A99

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