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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Branching processes with competition by pruning of
Levy trees - Berestycki\, J (University of Oxford
)
DTSTART;TZID=Europe/London:20150318T153000
DTEND;TZID=Europe/London:20150318T163000
UID:TALK58456AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58456
DESCRIPTION:Co-authors: Joaquin Fontbona (U. Chile)\, Maria Cl
ara Fittipaldi (U. Chile)\, L. Doering (U. Zurich)
\, L. Mytnik (Technion)\, L. Zambotti (UPMC) \n\nT
here are several ways to describe the evolution of
a population with no interactions between individ
uals. One approach is to use the local time proces
s of a forrest of Lvy trees\, or\, following the w
ork of Dawson and Li\, one can construct the whole
population flow as the solution to a certain syst
em of Lvy driven stochastic differential equation.
The equivalence between these two constructions i
s a generalization of the well-known Ray-Knight Th
eorem.\n \nWhen one wants to introduce a form of c
ompetition in the population\, the situation becom
es more involved. The stochastic differential appr
oach still works (with an added negative drift ter
m) and the purpose of this talk is to present a no
vel construction based on the interactive pruning
of the Lvy forrest.\n \nThe case of a positive dri
ft\, which corresponds to an interactive immigrati
on\, is also of interest as it is related to the q
uestion of existence of exceptional times for Gene
ralized Fleming-Viot processes with mutations at w
hich the number of genetic types in the population
is finite.\n \nBased on joint works with : a) L.
Doering\, L. Mytnik and L. Zambotti and b) J. Font
bona and M.C. Fittipaldi \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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