Measure-valued diffusion

Abstract

We consider the class of continuous measure-valued processes {μ _t } on a finite-dimensional Euclidean space X for which ∫fd μ _t is a semimartingale with absolutely continuous characteristics with respect to t for all f:X→R smooth enough. It is shown that, under some general condition, the Markov process with this property can be obtained as a weak limit for systems of randomly interacting particles that are moving in X along the trajectories of a diffusion process in X as the number of particles increases to infinity.