Random jumps and coalescence in the continuum: evolution of states of an infinite system

Abstract

The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space $\Gamma$ the evolution of which is constructed in the following way. The evolution of observables $F_0\to F_t$ is obtained from a Kolmogorov-type evolution equation. Then the evolution of states $\mu_0\to \mu_t$ is defined by the relation $\mu_0(F_t) =\mu_t(F_0)$ for $F_0$ belonging to a measure-defining class of functions. The main result of the paper is the proof of the existence of the evolution of this type for a bounded time horizon.