The convex minorant of the Cauchy process
type: Item
instance of: scholarly article
title: The convex minorant of the Cauchy process
zbMATH Open document ID: 0954.60042
published in: Electronic Communications in Probability
publication date: 2000-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/120779
full work available at URL: paper5.abs.html
review text: The author determines the law of the convex minorant (\(M_s\), \(s\in[0,1]\)) of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. For a given real-valued function \(f\) defined on some interval \(I\subseteq \mathbb{R}\), one calls the convex minorant of \(f\) the largest convex function on \(I\) which is bounded from above by \(f\). The author also proves that the paths of \(M\) have a continuous derivative, and that the support of the Stieltjes measure \(dM'\) has logarithmic dimension one.
Mathematics Subject Classification ID: 60G51
zbMATH DE Number: 1447309
zbMATH Keywords: Cauchy process
zbMATH Keywords: convex minorant
author: Jean Bertoin
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
DOI: 10.1214/ECP.V5-1017
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description: scientific article; zbMATH DE number 1447309