与年龄和漏记忆相关的Hawkes过程的平均场极限
Mean-field limit of Age and Leaky Memory dependent Hawkes processes
摘要：
我们提出了一个相互作用的点过程的平均场模型，其中每个过程都有一个记忆的时间流逝，因为它的最后一个事件（年龄）和最近的过去（泄漏记忆），广义依赖于霍克斯过程。该模型的动机是相互作用的非线性霍克斯过程与马尔可夫自相互作用和网络的尖峰神经元的适应和短期突触可塑性。通过证明混沌的传播和使用的极限过程的法律路径积分表示，我们表明，在平均场极限，系统的经验措施如下多维非局部输运方程。
英文摘要：
We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is motivated by interacting nonlinear Hawkes processes with Markovian self-interaction and networks of spiking neurons with adaptation and short-term synaptic plasticity. By proving propagation of chaos and using a path integral representation for the law of the limit process, we show that, in the mean-field limit, the empirical measure of the system follows a multidimensional nonlocal transport equation.
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