Evolution of states in a continuum migration model

Abstract

The Markov evolution of states of a continuum migration model is studied. The model describes an infinite system of entities placed in $\mathds{R}^d$ in which the constituents appear (immigrate) with rate $b(x)$ and disappear, also due to competition. For this model, we prove the existence of the evolution of states ${\mu }_0\mapsto {\mu }_t$ such that the moments ${\mu }_t(N_{\Lambda }^n)$, $n\in \mathds{N}$, of the number of entities in compact $Λ\subset \mathds{R}^d$ remain bounded for all $t>0$. Under an additional condition, we prove that the density of entities and the second correlation function remain bounded globally in time.

References in corpus (1)

• Regulation mechanisms in spatial stochastic development models