Markov Evolution of Continuum Particle Systems with Dispersion and Competition

Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky, Oleksandr Kutoviy

Published 2011-12-05, updated 2012-04-06Version 2

We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other (compete). The main result is a statement that the corresponding correlation functions evolve in a scale of Banach spaces and remain sub-Poissonian, and hence no clustering occurs, if the dispersion is subordinate to the competition.