Séminaire Jeunes chercheurs (Benjamin Massat, jeudi 19 mars 2026)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 19 mars 2026 à 17h en salle A707. Nous aurons le plaisir d'écouter Benjamin Massat (Institut Mathématique de Toulouse), qui nous parlera de

Quantification of limit theorem for nearly unstable Hawkes processes

Abstract
Hawkes processes are a popular model for self-exciting phenomena, from earthquakes to finance. In this talk, I will first present them in a simple way, using a Poisson imbedding construction. I will then review what is known about their long-time behavior, through limit theorems for both linear and non-linear cases. The focus will be on three regimes that appear when the process has a long memory and the branching ratio gets close to or above one: the Nearly Unstable, the Weakly Critical, and the Supercritical Nearly Unstable Hawkes processes. These regimes have been studied qualitatively, but quantitative convergence results have been missing. I will explain how we obtain explicit convergence rates, relying on a coupling with a Brownian sheet, Fourier analysis, and a careful approximation of the absolute value function.