Markov evolutions in spatial ecology: From microscopic dynamics to kinetics

Abstract

In this summary, we construct Markov statistical dynamics for a class of birth-and-death ecological models in the continuum. Mesoscopic scaling limits for these dynamics lead to the kinetic equations for the density of a population. The resulting evolution equations are non-local and non-linear ones. We study properties of solutions to kinetic equations which strongly depend on characteristics of the models considered.