Central limit theorem for a partially observed interacting system of Hawkes processes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Central limit theorem for a partially observed interacting system of Hawkes processes

Résumé

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 $\mu> 0$ and on the sum of some function $\phi$ of the ages of the actions of the individuals which influence him. The parameters $\mu$ and $\phi$ 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.

Dates et versions

hal-03886060 , version 1 (06-12-2022)

Identifiants

Citer

Chenguang Liu. Central limit theorem for a partially observed interacting system of Hawkes processes. 2022. ⟨hal-03886060⟩
1 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More