2023/04/13 by Ruíz, Luis Iván Hernández, Yano, Kouji
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2304.06288
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.