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SUMMARY:Growth of sub-Malthusian Crump--Mode--Jagers processes
DTSTART:20261117T085000Z
DTEND:20261117T095000Z
DTSTAMP:20261115T162700Z
UID:indico-event-17590@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jakob Stonner (Universität Gießen)\n\nIt is well-k
 nown that the number $N(t)$ of births in a Malthusian Crump--Mode--Jagers 
 process up to time $t \\geq 0$ typically grows asymptotically like $\\math
 rm{e}^{\\alpha t}$ where $\\alpha > 0$ is the abscissa where the Laplace t
 ransform $m$ of the intensity measure $\\mu$ of the reproduction point pro
 cess hits the level $1$.We consider the situation where $m(\\alpha) < 1$ a
 nd $m(\\theta) = \\infty$ for all $\\theta < 1$.We prove that under certai
 n assumptions (including Poisson reproduction) $N(t)$ grows like $\\mathrm
 {e}^{\\alpha t} F(t\,t+1]$ where $F(\\mathrm{d} x) = \\mathrm{e}^{-\\alpha
  x}\\mu(\\mathrm{d} x)$ is the exponential tilted intensity measure.\n\nht
 tps://indico.math.cnrs.fr/event/17590/
LOCATION:Salle Pellos (1R2 207)
URL:https://indico.math.cnrs.fr/event/17590/
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