Groupe de travail Probabilités et Statistique

Date possible pour le colloquinte

Dans ce groupe de travail, l’orateur presentera les grandes lignes de sa recherche actuelle et future.

In this Groupe de travail the speaker will present some ideas for current/future research.

Réunion d’équipe enseignements

9h10 Les organisateurs Introduction

9h15-9h50 Rémi Peyre Les QCM bayésiens.
9h55-10h30 Alexis Anagnostakis A strong joint invariance principle for the Conditional Moment Matching Random Walk.

11h00-11h35 Edouard Strickler Comportement du mouvement brownien conditionné au confinement d’une diffusion sur un intervalle.
11h40-12h15 Pascal Moyal Extensions du modèle d’appariement aléatoire: Impatience, et hypergraphes.

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

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!

Réunion d’équipe permanents