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SUMMARY:Computing the Wiener-Hopf factors for Levy processes: Lecture 1 - 
 Alexey  Kuznetsov (York University (Canada))
DTSTART:20190806T144500Z
DTEND:20190806T160000Z
UID:TALK128113@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Wiener-Hopf factorization is a fundamental result in the t
 heory of Levy processes\; it provides a wealth of information about the fi
 rst exit of the underlying process from a half-line. The main goal of thes
 e lectures is to show how to use complex-analytic methods to obtain explic
 it formulas for Wiener-Hopf factors for several important classes of Levy 
 processes. We will start with processes with jumps of rational transform\,
  then we will discuss the class of stable processes\, explaining how one c
 ould recover from the Wiener-Hopf factors the distribution of the supremum
  of the process at a fixed time. Finally\, we will talk about the difficul
 t problem of how a Levy process exits an interval\, which turns out to be 
 related to Wiener-Hopf factorization for certain 2x2 matrices. This latter
  problem is wide open for processes with double-sided jumps and we will di
 scuss what is currently known for stable processes.&nbsp\;   <br><br><br><
 br><br>
LOCATION:Seminar Room 1\, Newton Institute
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