Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Cet exposé rentre dans le cadre du séminaire de vulgarisation de la Fédération Normandie-Mathématiques.

Pour en savoir plus, consulter la page du séminaire

In the physical sciences, relaxation usually means the return of a perturbed system to equilibrium. Each relaxation process can be categorized by a relaxation time $\tau$, for a generic commercial grade ferrofluid (a mixture  of nanoscale ferromagnetic particles of a compound containing iron suspended in a fluid) the relaxation time is very small, of the order $\tau \sim 10^{-9}$; it makes hence sense to provide an asymptotic approximation when $\tau  \to 0$.

This work extends the link between stochastic approximation (SA) theory and randomized urn models, and their applications to clinical trials. We no longer assume that the drawing rule is uniform among the balls of the urn (which contains d colors), but can be reinforced by a function f which models risk aversion. Firstly, by considering that f is concave or convex and by reformulating the dynamics of the urn composition as an SA algorithm with emainder, we derive the a.s.

Étant donné un espace de décalage $G^\mathbb{Z}$, où $G$ est un groupe abélien fini, un automate cellulaire abélien (ACA) est un endomorphisme de $G^\mathbb{Z}$ défini «par blocs». Nous étudions l’action de ces ACA sur les mesures de probabilités sur $G^\mathbb{Z}$.

In this presentation we discuss various measures of divergence including a general class of power divergence measures and explore some of their properties.

Existence and uniqueness of strong solutions to nonlinear Fokker-Planck equations driven by linear multiplicative noise is studied.
This is a joint work with Michael Rockner.

This paper focuses on the study of an original combination of the Euler Multilevel Monte Carlo introduced by Giles  and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins-Monro type stochastic algorithms. On the one hand, we extend our previous work to the Multilevel Monte Carlo setting. On the other hand, we improve  by providing a new adaptive algorithm avoiding the discretization of any additional process.