Pure and Applied Mathematics Laboratory (LMPA)

Our research work focuses on limit theorems, convergence of stochastic processes and statistical applications. First, we are interested in the convergence in law of stochastic processes considered as random elements of Hölder space and, after establishing Hölderian invariance principles, in the study of the Hölderian convergence of empirical processes and quantile processes, because of their use in statistics, such as epidemic rupture detection. Next comes the Hölderian approximation of fractional Brownian motion by the Skorohod integral process and its various applications.

On the other hand, queuing and reliability theories are specialties of applied mathematics at the frontier between probability theory (and mathematical statistics) and operations research. Applications therefore cover a wide range of practical issues. The aim is to evaluate and control certain performance measures of the systems studied from different points of view, in order to guarantee Quality of Service (QoS). Firstly, in system performance modeling and evaluation problems (queuing, financial, etc.). An alternative to the complexity problems posed by algorithmic problems is the use of asymptotic techniques, which involve approximating the stationary distribution (when it exists) under certain assumptions about the parameters.