Statistical inference for a partially observed interacting system of Hawkes processes
schedule le lundi 25 novembre 2019 de 17h00 à 18h00
Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu
Intervenant : Chenguang Liu (LPSM)
Lieu : P7 Sophie Germain Room 1016
Sujet : Statistical inference for a partially observed interacting system of Hawkes processes
We observe the actions of a sub-sample of individuals, during some time interval with positive length, for some large K ≤ N. We model the relationships of individuals by i.i.d. Bernoulli(p) random variables, where 0 < p ≤ 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 function φ is unknown but we assume it rapidly decays. The aim of this thesis is to estimate the parameter, which is the main characteristic of the interaction graph, in the asymptotic where the population size N → ∞, the observed population size → ∞, and in large time t → ∞.