论文标题
年龄的平均范围限制和记忆依赖的霍克斯进程
Mean-field limit of Age and Leaky Memory dependent Hawkes processes
论文作者
论文摘要
我们提出了一个相互作用点过程的平均场模型，其中每个过程都有自上次事件（年龄）和最近的过去（泄漏记忆）以来经过的时间的记忆，从而概括了与年龄有关的霍克斯过程。该模型是通过将非线性鹰派工艺与马尔可夫的自我交互和具有适应性和短期突触可塑性的尖峰神经元网络相互作用的动机动机。通过证明混乱的传播并使用路径积分表示对极限过程的定律，我们表明，在均值场限制中，系统的经验度量遵循多维非局部传输方程。
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.
