The convex minorant of the Cauchy process
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.
scientific article; zbMATH DE number 1447309