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math.PR2024
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.…
math.PR2024
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…