From the 1 of 6 linked papers with an AI index.
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Central limit theorem for a partially observed interacting system of Hawkes processes I: subcritical case
Chenguang Liu, Liping Xu, An Zhang
We consider a system of Hawkes processes and observe the actions of a subpopulation of size up to time , where is large. The influence relationships between ea…
Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail
Liping Xu, An Zhang
In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context…
Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials
Chenguang Liu, Liping Xu, An Zhang
In this paper, we prove that the Kac stochastic particle system converges to the weak solution of the spatially homogeneous Boltzmann equation for hard potentials and hard spheres.…
Scaling limits for supercritical nearly unstable Hawkes processes
Chenguang Liu, Liping Xu, An Zhang
In this paper, we investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has norm strictly greater than one and close to one as time…