A continuum individual based model of fragmentation: dynamics of correlation functions

An individual-based model of an infinite system of point particles in ${\mathbb{R}}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set $\mathrm{\Gamma }$ of all locally finite subsets of ${\mathbb{R}}^d$. The system’s states are probability measures on $\mathrm{\Gamma }$ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.