Résumé
This habilitation deals with both theoretical and applied aspects of probability, mathematical statistics and computational statistics, including modelling for application to real data. The theoretical tools concerned are Markov chains, heavy-tailed laws and stable processes, spatial processes, stochastic differential equations with approaches to the existence of solutions, approximation and parametric or non-parametric estimation, and extreme value statistics. I am interested in mixing conditions, statistical inference, numerical approximation, spatial interpolation and machine learning. In terms of applications, I am interested in health-environment data (vector capture data for arboviroses and infectious diseases), epidemiology (Covid-19, Dengue fever, thyphoid fever, etc.), econometrics and quantitative finance (price variation).