PUB - Publikationen an der Universität Bielefeld

The Markov evolution of states of a continuum migration model is studied. The model describes an infinite system of entities placed in 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) -> mu(t) such that the moments mu(t) (N-Lambda(n)), n is an element of N, of the number of entities in compact Lambda subset of 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 point-wise bounded globally in time.