论文标题
霍克斯过程的稳定性
Stability for Hawkes processes with inhibition
论文作者
论文摘要
我们考虑了多级设置中的多元非线性鹰型过程，其中粒子在两个可能不同大小的种群中组织起来，因此其中一个人群在系统上起兴奋性，而其他种群在系统上抑制了抑制性。本注释的目的是提出一类具有稳定动力学的霍克斯过程，而没有对相关权重函数矩阵的光谱半径进行假设。这说明了霍克斯系统中的抑制作用如何显着影响系统的稳定性。
We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other population acts inhibitory on the system. The goal of this note is to present a class of Hawkes Processes with stable dynamics without assumptions on the spectral radius of the associated weight function matrix. This illustrates how inhibition in a Hawkes system significantly affects the stability properties of the system.
