Loglinear Hawkes processes

2025/07/15 by Tomasz R. Bielecki, Bielecki, Tomasz R., Jacek Jakubowski +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2507.11265

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

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.

Citations

• Fluctuations and moderate deviations for the mean fields of Hawkes processes
• Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition
• Long time behavior of an age and leaky memory-structured neuronal population equation
• Renewal in Hawkes processes with self-excitation and inhibition
• Stability, convergence to equilibrium and simulation of non-linear\n Hawkes Processes with memory kernels given by the sum of Erlang kernels
• Multi-class oscillating systems of interacting neurons
• Nonlinear Hawkes Processes

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