307
Views
1
CrossRef citations to date
0
Altmetric
Research Article

An extension of Hawkes processes with ephemeral nearest effects

&
Pages 335-366 | Received 29 Apr 2020, Accepted 21 Jan 2021, Published online: 16 Feb 2021
 

Abstract

Hawkes processes have been widely studied in both theory and applications because of their self-exciting effects, but there are still some questions and room left for exploring the self-exciting point processes. In this paper, an ephemeral self-exciting Hawkes process is developed, which contains 1-memory and 0-memory self-exciting point processes. After giving the definition of the ephemeral self-exciting Hawkes process, some explanations on this new point process, properties, declustering of the occurrences of events, positive and negative self-exciting effects are presented. Moments of this point process are derived as well in the paper by using the Laplace transforms and the elementary method. Some special cases are considered and the computation methods of moments are also presented by the difference method and inverse Laplace transforms, respectively. Combining dynamics of the self-exciting point process and the delayed renewal process is an important feature of the proposed ephemeral self-exciting Hawkes process, which may shed light on the related studies in the future.

Acknowledgements

The authors also thank two anonymous referees for their suggestions for improving the paper.

Additional information

Funding

This work is supported by the NSF of China under grants 71871021 and 71631001.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,125.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.