A cluster representation of the renewal Hawkes process
Probability
2025-07-01 v2
Abstract
A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed construction indeed represents a cluster process and it is verified that it admits the desired intensity. Finally, the probability generating functional is computed for the stationary limit case.
Keywords
Cite
@article{arxiv.2304.06288,
title = {A cluster representation of the renewal Hawkes process},
author = {Luis Iván Hernández Ruíz and Kouji Yano},
journal= {arXiv preprint arXiv:2304.06288},
year = {2025}
}