Loglinear Hawkes processes
Probability
2025-07-16 v1
Abstract
This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. In the main theorem, we give sufficient conditions for explosion and nonexplosion that cover a large class of practically relevant memory functions. We also investigate stability. In particular, we show that for nonpositive memory functions the loglinear Hawkes process is stable. The paper aims at providing a theoretical basis for further research and applications of these processes.
Keywords
Cite
@article{arxiv.2507.11265,
title = {Loglinear Hawkes processes},
author = {Tomasz R. Bielecki and Jacek Jakubowski and Matthias Kirchner and Mariusz Niewęgłowski},
journal= {arXiv preprint arXiv:2507.11265},
year = {2025}
}
Comments
18 pages