Bertoin, Jean The convex minorant of the Cauchy process. (English) Zbl 0954.60042 Electron. Commun. Probab. 5, 51-55 (2000). 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. Reviewer: Zdzislaw Rychlik (Lublin) Cited in 12 Documents MSC: 60G51 Processes with independent increments; Lévy processes Keywords:Cauchy process; convex minorant × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS