Long-time asymptotics for multivariate Hawkes processes with long-range interactions
Probability
2026-03-09 v1
Abstract
We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent Our main focus is on the long-time asymptotic behavior of the system. The proofs of our results combine techniques developed for short-range interactions, properties of -stable laws, and a Tauberian theorem. This model is more intricate and realistic for some applications, such as neural networks, where long-range connections are present.
Cite
@article{arxiv.2603.05853,
title = {Long-time asymptotics for multivariate Hawkes processes with long-range interactions},
author = {Nadia Belmabrouk},
journal= {arXiv preprint arXiv:2603.05853},
year = {2026}
}