Benjamin Massat

Far from the thankless, pointless exercises they are often thought to be, [...] mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.
— Alain Badiou

About me

Since September 2023, I am a PhD student at the Institut de Mathématiques de Toulouse (IMT) under the supervision of Laure Coutin and Anthony Réveillac. I am also a teacher instructor at INSA.

My research focuses on applied mathematics, with a particular interest in probability theory — a field I discovered during my undergraduate studies and have been passionate about ever since.

Driven by a long-standing interest in mathematics and its applications, I aim through my thesis to contribute to the theoretical understanding of stochastic models and their practical implications. In particular, my PhD focuses on the study of limit theorems for Hawkes processes.

Curriculum Vitae

Formation

I completed a two-year intensive preparatory program in mathematics and physics (MPSI/MP) at Lycée Sainte-Croix – Sainte-Euverte in Orléans. This experience provided me with a strong foundation in theoretical mathematics and helped nurture my curiosity and rigor in scientific thinking.

2017-2019 : CPGE MPSI/MP

I pursued a Bachelor's degree in Applied Mathematics at the University of Orléans. It was during this time that I discovered a strong interest in research, particularly through courses that combined mathematical theory with real-world applications.
2019 : Bachelor Degree

I completed two Master’s degrees at the University of Toulouse — one focused on preparation for the agrégation in mathematics, and another in Research and Innovation. I obtained the agrégation in mathematics in the same period. I am now a PhD student at the Institut de Mathématiques de Toulouse, working in applied mathematics and probability theory.
2020-2022 : Master for the Agrégation
2022-2023 : Master R&I
2023-now : PhD

If you want to know more about my background and education, click here to download my resume: Curriculum Vitae

Research

Publications and Preprints

Quantification of limit theorems for Hawkes processes

Laure Coutin, Benjamin Massat & Anthony Réveillac

In this article, we fill a gap in the literature regarding quantitative functional central limit theorems (qfCLT) for Hawkes processes by providing an upper bound for the convergence of a nearly unstable Hawkes process toward a Cox-Ingersoll-Ross (CIR) process. Note that in this case no speed of convergence has been established even for one-dimensional marginals; we provide in this paper a control in terms of a supremum norm in 2-Wasserstein distance. To do so, we make use of the so-called Poisson imbedding representation and provide a qfCLT formulation in terms of a Brownian sheet. Incidentally, we construct an optimal coupling between a rescaled bi-dimensional Poisson random measure and a Brownian sheet with respect to the 2-Wasserstein distance and analyze the asymptotic quality of this coupling in detail.

Quantification of limit theorems for Hawkes processes

Normal approximation of Functionals of Point Processes: Application to Hawkes Processes

Laure Coutin, Benjamin Massat & Anthony Réveillac

In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson imbedding representation, our result applies to a variety of point processes including discrete and continuous Hawkes processes. In particular, we establish an explicit convergence rate for stable continuous non-linear Hawkes processes and for discrete Hawkes processes. Finally, we obtain an upper bound in the context of nearly unstable Hawkes processes.

Normal approximation of Functionals of Point Processes: Application to Hawkes Processes

Teaching

Eng'INSA

I currently teach mathematics at INSA Toulouse, where I give both lectures and tutorials. On this page, I provide access to the course materials, exercises, and past exam papers I use in class. These resources are freely available to help students review and prepare throughout the semester.

Lectures

Tutorials

Exam