Markov Evolution of Continuum Particle Systems with Dispersion and Competition

Abstract

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.

43 pages

Cited by in corpus (1)

• Stochastic evolution of a continuum particle system with dispersal and competition: micro- and mesoscopic description