Virgile Brodu

A result of convergence for measure-valued processes

First, we introduce càdlàg measure-valued processes, with biological motivations. We focus on the construction with Poisson point measures and the useful martingale properties it entails. Then, we present a general convergence result for these measure-valued processes. In the literature, such a convergence result is proven with bounded growth, birth and death rates. We present a more general framework with unbounded rates, where the convergence still holds true in a weighted space of measures. This is joint work with Nicolas Champagnat and Coralie Fritsch.