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.