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math.DS2025
Local stability and rates of convergence to equilibrium for the Nonlinear Renewal Equation; applications to Hawkes processes
Céline Duval, Eric Luçon
We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results ar…
math.PR2025
Neural Field Equations and Hawkes processes: long-term stability of traveling wave profiles in the neutral case
Eric Luçon, Christophe Poquet
We consider the long-time behavior of a population of interacting Hawkes processes on the real line, with spatial extension. The large population behavior of the system is governed…