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

06/19/2019

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by   Chenguang Liu, et al.

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We observe the actions of a K sub-sample of N individuals up to time t for some large K< N. We model the relationships of individuals by i.i.d. Bernoulli(p)-random variables, where p∈ (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 D, both in the subcritical and supercritical cases.