部分可观测Hawkes过程相互作用系统的中心极限定理
Central limit theorem for a partially observed interacting system of Hawkes processes
摘要：
我们观察$K$子样本的$N$个人的行动，直到一些大的$K\le N$的时间$t$。我们用i.i.d.来模拟个体之间的关系。Bernoulli（$p$）-随机变量，其中$p\in (0,1]$是未知参数。每个人的行动速率取决于某个未知参数$μ> 0$和某个影响他的个体行动年龄的函数$ϕ$的和。参数$μ$和$ϕ$被认为是多余参数。本文的目的是获得一个中心极限定理的估计$p$，我们介绍了\cite{D}，在亚临界和超临界的情况下。
英文摘要：
We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$ for some large $K\le N$. We model the relationships of individuals by i.i.d. Bernoulli($p$)-random variables, where $p\in (0,1]$ is an unknown parameter. The rate of action of each individual depends on some unknown parameter $μ> 0$ and on the sum of some function $ϕ$ of the ages of the actions of the individuals which influence him. The parameters $μ$ and $ϕ$ are considered as nuisance parameters. The aim of this paper is to obtain a central limit theorem for the estimator of $p$ that we introduced in \cite{D}, both in the subcritical and supercritical cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
