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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Theory of Bernstein-Gamma functions and asymptotic
s of densities of exponential functionals of subor
dinators - Mladen Savov (Sofia University St. Klim
ent Ohridski\, Bulgarian Academy of Sciences)
DTSTART;TZID=Europe/London:20220307T100000
DTEND;TZID=Europe/London:20220307T110000
UID:TALK170033AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170033
DESCRIPTION:Asymptotics of densities of exponential functional
s of subordinators\nAbstract: In this talk we are
going to present \; a new class of special fun
ctions that we call Bernstein-Gamma functions.\nBe
ing a natural extension of the classical Gamma fun
ction these functions play a role in the study of\
nsome Markov self-similar processes and for these
reason they have also appeared in fractional\ncalc
ulus as an extension of Caputo&rsquo\;s derivative
. We shall make an overview of the current underst
anding of the properties of Bernstein-Gamma functi
ons. \;We are going to employ these \; fu
nctions for the study the large asymptotic of dens
ities of exponential functionals of subordinators.
The intense study of exponential functionals of L
́evy processes\nhas been triggered by the differe
nt applications these quantities have both in theo
retical and\napplied studies. Gradually\, their la
rge asymptotic has been almost completely understo
od with\nthe omission of the case when the underly
ing L ́evy processes is a subordinator. This is du
e to the\nfact that the asymptotic is non-classica
l from Tauberian point of view. The method we empl
oy\nis based on the saddle point method which invo
lves the fine understanding of the Stirling-type\n
asymptotic of \; the \; Bernstein-Gamma fu
nctions.\nThis is joint work with Martin Minchev
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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