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BEGIN:VEVENT
DTSTAMP:20260427T175455Z
DTSTART;VALUE=DATE-TIME:20230124T170000
DTEND;VALUE=DATE-TIME:20230124T180000
SUMMARY:YRM - Aria Ahari on boundary crossing problems and functional tra
 nsformations for Ornstein-Uhlenbeck processes
TZID:Europe/London
UID:20230124-8a17841a857d1aeb0185829315d70ca9@warwick.ac.uk
CREATED:20230119T205811Z
DESCRIPTION:Title: Boundary crossing problems and functional transformati
 ons for Ornstein-Uhlenbeck processes Abstract: We are interested in the 
 law of the first passage time of driftless Ornstein-Uhlenbeck processes 
 to time varying thresholds. We show that this problem is connected to th
 e law of the first passage time of the process to some two-parameter fam
 ily of functional transformations which\, for specific values of the par
 ameters\, appears in a realisation of a standard Ornstein-Uhlenbeck brid
 ge. We provide three different proofs of this connection. The first proo
 f is based on a similar result to the case of the Brownian motion\, the 
 second uses a generalisation of the so-called Gauss-Markov processes and
  the third relies on the Lie group symmetry method applied to the Fokker
 -Planck equation of the Ornstein-Uhlenbeck process. We investigate the p
 roperties of this transformation and study the algebraic and analytical 
 properties of an involution operator which is used in constructing it. W
 e also show that this transformation maps the space of solutions of Stur
 m-Liouville equations into the space of solutions of the associated nonl
 inear ordinary differential equations. Lastly\, we discuss the interpret
 ation of such transformations through the method of images and give new 
 examples of curves with explicit first passage time densities.
LOCATION:
CATEGORIES:
LAST-MODIFIED:20230119T205811Z
ORGANIZER;CN=Claudia Viaro:
END:VEVENT
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