*Mathematical Methods in the Applied Sciences*Dynamics of an infinite age-structured particle system

The Markov evolution is studied of an infinite age-structured population
of migrants arriving in and departing from a continuous habitat $X
\subseteq\mathds{R}^d$ – at random
and independently of each other. Each population member is characterized
by its age $a\geq 0$ (time of presence in the
population) and location $x\in X$. The population
states are probability measures on the space of the corresponding marked
configurations. The result of the paper is constructing the evolution
$\mu_0 \to \mu_t$ of
such states by solving a standard Fokker-Planck equation for this
models. We also found a stationary state $\mu$ existing
if the emigration rate is separated away from zero. It is then shown
that $\mu_t$ weakly converges to
$\mu$ as $t\to
+\infty$.

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