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arXiv · 1607.05871

Evolution of states in a continuum migration model

Yuri Kondratiev·Yuri Kozitsky
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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 $\Lambda \subset \mathds{R}^d$ 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.

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Yuri Kondratiev, Yuri Kozitsky. 2016-07-20. Evolution of states in a continuum migration model. https://arxiv.org/abs/1607.05871

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