The Convex Minorant of the Cauchy Process
Jean Bertoin, Universite Pierre et Marie Curie
Abstract
We determine the law of the convex minorant $(M_s,
sin [0,1])$ 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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