arXiv subjects

Théo Leblanc

Publications and source records attributed to Théo Leblanc.

3 recordsLinked to original sources

arXiv2026

Exponential Tail Estimates for Multitype Poisson Branching Processes and Application to Hawkes Processes

We establish exponential moment bounds for linear functionals of the total progeny of multitype Poisson Bienaymé-Galton-Watson trees. Our estimates are explicitly characterized in terms of the offspring mean matrix and the coefficients of the linear functional. As an application, we derive type-specific exponential moment bounds for multitype Hawkes processes, yielding improved results in high-dimensional settings. We also obtain exponential tail estimates for inhomogeneous Poisson clusters, with bounds that reflect the decay properties of the interaction kernels defining the clusters. These results provide useful probabilistic tools for the analysis of branching structures arising in Hawkes processes and related models.

math.PR↗

arXiv2026

Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes

Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at different time scales, it is natural to study multiscale and heterogeneous processes, such as those obtained by combining Hawkes and autoregressive dynamics. In this paper, we introduce this new Hawkes autoregressive (HAR) model incorporating both continuous- and discrete-time dynamics, and establish several probabilistic results, including the existence of a stationary version, a cluster representation, as well as stability and ergodic properties.

math.PR↗

arXiv2025

Exponential moments for Hawkes processes under minimal assumptions

We prove that the number of points of a stationary linear Hawkes process lying in any bounded subset of the real line has exponential moments, without any other assumption than the one needed for existence of such stationary process, namely the spectral radius of the matrix of L1 norms of interaction functions is smaller than one. The proof relies on a mass transport principle argument. We also specify the dependence of the bounds with respect to the base rates and the matrix of L1 norms of interaction functions defining the Hawkes process and give a functional version of the result.

math.PR↗