Conférenciers

 Comparing Random Variables: The Theory and Applications of Stochastic Orders

In this plenary talk, I will provide a comprehensive overview of stochastic orders, which are fundamental concepts in probability theory used to compare the relative magnitudes, size, and skewness of random variables. Stochastic orders provide a systematic way to order random variables based on their probability distributions, and they have found important applications in various fields such as finance, economics, actuarial science, and reliability engineering.

During my talk, I will delve into the theory behind stochastic orders, including their definition, properties, and several interesting results that have been obtained in this area of research. I will also demonstrate the practical applications of stochastic orders in real-world settings, such as modeling risk in financial portfolios, analyzing the aging process of different systems, evaluating the performance of complex systems, and more.

Multiples solutions pour le système de Gierer-Meinhardt

Dans cet exposé, nous présentons des propriétés quantitatives et qualitatives des solutions du système de Gierer-Meinardt. Nous obtenons l'existence d'au moins trois solutions distinctes en fournissant des informations précises sur leur signe. Nous montrons que, sous l'hypothèse que le système est soumis à la condition aux limites de Neumann, ces solutions sont toutes positives tandis que, dans le cas de Dirichlet, deux d'entre elles sont de signe constant et opposé, et la troisième est nodale (i.e., de signe changeant). L'approche utilisée est basée essentiellement sur la méthode des sous-et-sur-solutions ainsi que le degré topologique de Leray-Schauder.

Asymptotic for sums of random variables 

Summing random variables is one of the most common operations performed by probabilists and statisticians. It is just natural that one is interested in their asymptotic behaviour, especially when weights are considered i the summations. We will take an overview of convergence assumptions, linking moment properties and weight behaviour, for independent variables and also considering some dependence structure on the variables and how to control it.

Investigating spatial scan statistics for multivariate functional data

In environmental surveillance, cluster detection of environmental black spots is of major interest due to the adverse health effects of pollutants, as well as their known synergistic effect. Thus, this paper introduces new spatial scan statistics for multivariate functional data, applicable for detecting clusters of abnormal air pollutants concentrations measured spatially at a very fine scale in northern France in October 2021 taking into account their correlations.

Mathematically, our methodology  is derived from a functional multivariate analysis of variance (MANOVA), an adaptation of the Hotelling $T^2$-test statistic, and a multivariate extension of the Wilcoxon test statistic. The approaches were evaluated in a simulation study and then applied to the air pollution dataset.

Strong uniform consistency of the local linear  relative error regression estimator under left truncation 

This paper is concerned with a nonparametric estimator of the regression function based on the local linear method when the loss function is the mean squared relative error and the data left truncated. The proposed method avoids the problem of boundary effects and is robust against the presence of outliers. Under suitable assumptions, we establish the uniform almost sure strong consistency with a rate over a compact set. A simulation study is conducted to comfort our theoretical result. This is made according to different cases, sample sizes, rates of truncation, in presence of outliers and a comparison study is made with respect to classical, local linear and relative error estimators. Finally, an experimental prediction is given.

Differential equations and population dynamics 

Many researchers are interested to the dynamic of predator-prey interactions mo[1]dels, and have investigated the processes that affect it. In this work we discuss a prey-predator model where one species is subjected to non-smooth harvesting effort and where both species are subjected to nonlinear harvesting. The models are modified versions from the classic Lotka[1]Voltera predator-prey model. To enrich the Lotka-Voltera model, many researchers modify the nonlinear functional response function and adding some other elements like, pollution, toxicity, harvesting, age of the species, refuge,...etc. Because that harvesting is an important and effective prevention and control means of the explosive growth of predators or prey when they are enough, it is reasonable to introduce the harvest of some species of populations into models. Researches on the effects of harvesting in fishery models are becoming more valuable and we focus in this work on the predator-prey models with harvest. Several forms and types of harvesting in prey-predator models are already being studied ; researchers have added terms to the prey or predator density like constants ; function that is linear if the density of the predator is bellow a switched value and constant otherwise ; functions of the form QiFixi/ (Qi + Fixi), i = 1, 2 where Qi and Fi are constants and xi , i = 1, 2 are the sizes of prey and predator populations respectively ; or recently a function constructed by incorporating the Heaviside function. These types of harvesting rates have their own advantages as well as disadvantages in the award of the harvest in the real world. Motivated by these view, we consider a predator-prey model with other forms of harvesting rate. Thus, it is interesting to construct new kind of harvesting rates and see what is going on for the density of prey and predator. The purpose of the work is to offer mathematical analysis of the models. The dynamical behaviors of the proposed models are examined.