A criterion of convergence of measure‐valued processes: application to measure branching processes

Abstract

In this paper martingale properties of a Measure Branching process are investigated. Uniqueness and continuity of this process are proven by a martingale approach. For the existence, we approximate the measure branching process by a sequence of infinite particle branching diffusion processes, and show the convergence in distribution by a new criterion for measure‐valued processes. We also give properties about local structure of the process.