Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum

Abstract

Two coupled spatial birth-and-death Markov evolutions on ${\mathbb{R}}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions satisfying the so-called Ruelle-bound. Using the general scheme of Vlasov scaling we are able to derive a system of non-linear, non-local mesoscopic equations describing the effective density of the particle system. The results are applied to several models of ecology and biology.

Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=914

References in corpus (1)

• Spatial birth and death processes as solutions of stochastic equations

Cited by in corpus (1)

• Stochastic averaging for a spatial population model in random environment