# Wednesday, August 21, 2019 - 15:00 in V2-213

From Gaussian estimates for nonlinear evolution equations to long time behavior of branching processes

A talk in the Bielefeld Stochastic Summer series by
Lucian Beznea from Romanian Academy, Bucharest

 Abstract: We study solutions to a nonlinear evolution equation in $R^d$, associated to a branching process. First, we deal with existence, uniqueness, and the asymptotic behavior of the solutions when the time tends to infinity. It turns out that the distribution of the associated branching process behaves, when the time tends to infinity, like that of the Brownian motion on the set of all finite configurations of $R^d$. However, due to the lack of conservation of the total mass of the initial non linear equation, a deformation with a multiplicative coefficient occurs. Finally, we establish asymptotic properties of the occupation time of this branching process. The talk is based on a joint work with Liviu I. Ignat and Julio D. Rossi. Within the CRC this talk is associated to the project(s): A5, B1, B2

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