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SUMMARY:Theory of Bernstein-Gamma functions and asymptotics of densities o
 f exponential functionals of subordinators - Mladen Savov (Sofia Universit
 y St. Kliment Ohridski\, Bulgarian Academy of Sciences)
DTSTART:20220307T100000Z
DTEND:20220307T110000Z
UID:TALK170033@talks.cam.ac.uk
DESCRIPTION:Asymptotics of densities of exponential functionals of subordi
 nators\nAbstract: In this talk we are going to present&nbsp\; a new class 
 of special functions that we call Bernstein-Gamma functions.\nBeing a natu
 ral extension of the classical Gamma function these functions play a role 
 in the study of\nsome Markov self-similar processes and for these reason t
 hey have also appeared in fractional\ncalculus as an extension of Caputo&r
 squo\;s derivative. We shall make an overview of the current understanding
  of the properties of Bernstein-Gamma functions. &nbsp\;We are going to em
 ploy these&nbsp\; functions for the study the large asymptotic of densitie
 s of exponential functionals of subordinators. The intense study of expone
 ntial functionals of L ́evy processes\nhas been triggered by the differen
 t applications these quantities have both in theoretical and\napplied stud
 ies. Gradually\, their large asymptotic has been almost completely underst
 ood with\nthe omission of the case when the underlying L ́evy processes i
 s a subordinator. This is due to the\nfact that the asymptotic is non-clas
 sical from Tauberian point of view. The method we employ\nis based on the 
 saddle point method which involves the fine understanding of the Stirling-
 type\nasymptotic of&nbsp\; the&nbsp\; Bernstein-Gamma functions.\nThis is 
 joint work with Martin Minchev
LOCATION:Seminar Room 2\, Newton Institute
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