Orateur : Félix Cheysson (Univ. Gustave Eiffel)
Hawkes processes are a family of point processes for which the occurrence of any event increases the probability of further events occurring. Although the linear Hawkes process, for which a representation in the form of a superposition of branching processes exists, is particularly well studied, difficulties remain in estimating the parameters of the process from imperfect data (noisy, missing or aggregated data), since the usual estimation methods based on maximum likelihood or least squares do not necessarily offer theoretical guarantees or are numerically too costly.
In this work, we propose a spectral approach well-adapted to this context, for which we prove consistency and asymptotic normality. In order to derive these properties, we show that Hawkes processes can be studied through the scope of mixing, opening the use of central limit theorems that already exist in the literature. I will then present two applications of this approach: to aggregated data (joint work with Gabriel Lang); and to noisy data (joint work with Anna Bonnet, Miguel Martinez and Maxime Sangnier).