The Convex Minorant of the Cauchy Process

Jean Bertoin (Universite Pierre et Marie Curie)

Abstract


We determine 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. In particular, this enables us to deduce that the paths of $M$ have a continuous derivative, and that the support of the Stieltjes measure $dM'$ has logarithmic dimension one.

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Pages: 51-55

Publication Date: January 20, 2000

DOI: 10.1214/ECP.v5-1017

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