Some limit theorems for locally stationary Hawkes processes
Probability
2025-01-30 v1
Abstract
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by recombining classical martingale methods introduced in Bacry et al. [3] with novel ideas proposed by Kwan et al. [19]. The asymptotic theory we obtain yields useful applications in financial statistics. As an illustration, we derive closed-form expressions for price distortions under liquidity constraints.
Keywords
Cite
@article{arxiv.2501.17245,
title = {Some limit theorems for locally stationary Hawkes processes},
author = {Thomas Deschatre and Pierre Gruet and Antoine Lotz},
journal= {arXiv preprint arXiv:2501.17245},
year = {2025}
}