Probabilities and Statistic working group

Réunion d’équipe permanents

What happens if we want to study the convergence of discontinuous real-valued stochastic processes, which is often the case for modelling purposes? For example, think of tracking the evolution of the population size of living species, where deaths are instantaneous negative jumps… In 1956, Skorokhod proposed a topology on the space of discontinuous functions, which is predominant today. The aim of this talk is to explain the simple and intuitive ideas underlying the construction of Skorokhod to facilitate its understanding, without going in the depth of technical proofs. If we have time, we will introduce measure-valued processes, with biological motivations, and explain how the Skorokhod construction can be generalized to more complex spaces such as these measure spaces.

Even if the present talk is self-contained, it can be seen as an introduction to the GdT of May, 22. I will also present my work about measure-valued processes during the GdT SIMBA of April, 24 (14h, Salle de Conférences). You are warmly welcome to attend one of these to discover some of my PhD research!

First, we introduce c`adl`ag 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. We insist on the topological
difficulties encountered, related to Skorokhod spaces. Thus, even if it is self-contained, this talk can
be seen as a natural continuation of the GdT of May, 15.
Note that I also present this work during the GdT SIMBA on April, 24 (14h, Salle de Conf´erences),
with a focus on the new results we obtain compared to the existing literature. This is joint work with
Nicolas Champagnat and Coralie Fritsch

Nous cherchons des orateurs

Réunion d’équipe enseignements