Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

On étudie un problème inverse consistant à déterminer des paramètres d'équations de type advection-réaction-diffusion, décrivant l'évolution de la concentration ou de la quantité d'une substance (par exemple d'un polluant dans l'air ou dans l'eau), à partir de mesures du flux généré par ce processus sur le bord d'un domaine prédéfini.

Abstract: We establish the Besov-Orlicz path regularity of the Lei-Nualart process. This immediately implies that any Gaussian process admitting a decomposition in law as the sum of a fractional Brownian motion and a Lei-Nualart process inherits the Besov-Orlicz regularity of its fractional Brownian motion component.

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts.

The construction of exible parametric distributions with prescribed properties is a classical problem in statistical distribution theory. In this talk, we present a recently introduced framework for generating broad families of continuous univariate distributions $[1, 2].$ The main idea is to represent the cumulative distribution function in the form  $$F(x) = g^{-1}(h(x)), \quad \quad  x > 0,$$

L'optimisation de fonctions convexes lisses dans un cadre stochastique, où seules des estimations bruitées des gradients et des Hessiennes sont disponibles, est un problème classique en statistique computationnelle. Si les méthodes de premier ordre possèdent un faible coût par itération, leur convergence peut s'avérer lente pour les problèmes mal conditionnés.

In this talk, we study notions of distances between graphs and their connections to optimal transport and combinatorial optimization. We focus in particular on graph edit distance and its relation to the Quadratic Assignment Problem (QAP), which provides a natural formulation for graph matching under structural constraints. We then introduce optimal transport-based distances, especially the Wasserstein distance and its extension to metric measure spaces via the Gromov–Wasserstein distance.

This work falls within the field of statistical modeling of extreme values, a fundamental area for the analysis and prediction of rare events with potentially severe consequences in domains such as finance, engineering, and natural risk management. Its main objective is to propose a flexible method for estimating extreme conditional quantiles.

We study a nonparametric regression model with circular responses in the presence of measurement errors in the covariates. The response variable takes values on the unit circle S1, while the predictors are observed through additive noise, leading to a statistical inverse problem.

The detection of disruptions in stochastic processes has evolved from early control charts to rigorous optimal stopping frameworks and modern adaptive systems. The classical procedures like CUSUM and Shiryaev’s rule set performance benchmarks and continue to inspire extensions to dependent, high-dimensional, and uncertain settings. The numerous application areas span industry, finance, engineering, cybersecurity, environmental protection, and healthcare, with a particularly significant impact on epidemiological surveillance.