Abstract
In this paper, we study an infinite system of point entities in ℝd which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is described by means of a BBGKY-type equation for the corresponding correlation (moment) functions. It is proved that: (a) these functions evolve on a bounded time interval and remain sub-Poissonian due to the competition; (b) in the Vlasov scaling limit they converge to the correlation functions of the time-dependent Poisson point field the density of which solves the kinetic equation obtained in the scaling limit from the equation for the correlation functions. A number of properties of the solutions of the kinetic equation are also esta- blished.
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