Abstract
We study the Markov dynamics of an infinite birth-and-death system of point
entities placed in $R^d$, in which the constituents disperse and die,
also due to competition. Assuming that the dispersal and competition kernels
are just continuous and integrable we prove that the evolution of states of
this model preserves their sub-Poissonicity, and hence the local
self-regulation (suppression of clustering) takes place. Upper bounds for the
correlation functions of all orders are also obtained for both long and short
dispersals, and for all values of the intrinsic mortality rate $m0$.
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