The Markov evolution of states of a continuum migration model is studied.
The model describes an infinite system of entities placed in Rd 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 μ0 → μt such that
the moments μt(N n ), n ∈ N, of the number of entities in compact  ⊂ Rd remain
bounded for all 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.

EB00000002876K

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• Evolution of states in a continuum migration model