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arXiv · 2304.06288

A cluster representation of the renewal Hawkes process

Luis Iván Hernández Ruíz·Kouji Yano
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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.

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Luis Iván Hernández Ruíz, Kouji Yano. 2023-04-13. A cluster representation of the renewal Hawkes process. https://arxiv.org/abs/2304.06288

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