Bernstein-gamma functions and exponential functionals of Lévy processes

Vortrag von Dr. Martin Minchev

Datum: 08.10.25  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

Bernstein-gamma (BG) functions, introduced by Patie 
and Savov (and also considered in earlier works by 
Berg, Bertoin, Hirsch, Yor, and others), solve a 
gamma-type recurrence with a Bernstein function in 
place of the identity. Their relevance for studying 
exponential functionals of Lévy processes stems from 
the fact that the Mellin transform of an EF factors 
through BG functions. This representation lets us 
extract asymptotics via Mellin inversion, Tauberian 
arguments, and links to Wiener-Hopf factors, and, 
in some cases, it yields weak limits for suitably 
scaled EF laws. We will sketch some concrete arguments 
and discuss how these ideas could extend to Markov 
additive processes through a matrix- or operator-valued 
analogue of BG functions, noting new obstacles.

Joint work with Mladen Savov.