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SUMMARY:Convex minorants and the fluctuation theory of Lévy processes - J
 orge Gonzalez-Cazares (University of Warwick\, The Alan Turing Institute)
DTSTART:20220421T140000Z
DTEND:20220421T143000Z
UID:TALK171425@talks.cam.ac.uk
DESCRIPTION:We establish a novel characterisation of the law of the convex
  minorant of any L&eacute\;vy process. Our self-contained elementary proof
  is based on the analysis of piecewise linear convex functions and require
 s only very basic properties of L&eacute\;vy processes. Our main result pr
 ovides a new simple and self-contained approach to the fluctuation theory 
 of L&eacute\;vy processes\, circumventing local time and excursion theory.
  Easy corollaries include classical theorems\, such as Rogozin's regularit
 y criterion\, Spitzer's identities and the Wiener-Hopf factorisation.
LOCATION:Seminar Room 1\, Newton Institute
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