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SUMMARY:Branching processes with competition by pruning of Levy trees - Be
 restycki\, J (University of Oxford)
DTSTART:20150318T153000Z
DTEND:20150318T163000Z
UID:TALK58456@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Joaquin Fontbona (U. Chile)\, Maria Clara Fittipal
 di (U. Chile)\, L. Doering (U. Zurich)\, L. Mytnik (Technion)\, L. Zambott
 i (UPMC) \n\nThere are several ways to describe the evolution of a populat
 ion with no interactions between individuals. One approach is to use the l
 ocal time process of a forrest of Lvy trees\, or\, following the work of D
 awson and Li\, one can construct the whole population flow as the solution
  to a certain system of Lvy driven stochastic differential equation. The e
 quivalence between these two constructions is a generalization of the well
 -known Ray-Knight Theorem.\n \nWhen one wants to introduce a form of compe
 tition in the population\, the situation becomes more involved. The stocha
 stic differential approach still works (with an added negative drift term)
  and the purpose of this talk is to present a novel construction based on 
 the interactive pruning of the Lvy forrest.\n \nThe case of a positive dri
 ft\, which corresponds to an interactive immigration\, is also of interest
  as it is related to the question of existence of exceptional times for Ge
 neralized Fleming-Viot processes with mutations at which the number of gen
 etic types in the population is finite.\n \nBased on joint works with : a)
  L. Doering\, L. Mytnik and L. Zambotti and b) J. Fontbona and M.C. Fittip
 aldi \n
LOCATION:Seminar Room 1\, Newton Institute
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