The Markov evolution of states of a continuum migration model is studied. The model describes an infinite system of entities placed in $${\mathbbm {R}}^d$$ 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 $$\mu _0 \mapsto \mu _t$$ μ 0 ↦ μ t such that the moments $$\mu _t(N_\Lambda ^n)$$ μ t ( N Λ n ) , $$n\in {\mathbbm {N}}$$ n ∈ N , of the number of entities in compact $$\Lambda \subset {\mathbbm {R}}^d$$ Λ ⊂ R d remain bounded for all $$t>0$$ t > 0 . Under an additional condition, we prove that the density of entities and the second correlation function remain point-wise bounded globally in time.
Analysis and Mathematical Physics – Springer Journals
Published: Mar 1, 2017
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