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A cluster process representation of a self-exciting process
Abstract
It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.
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Citations
Cited by
Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes
Ogata, Y. (1988) · Journal of the American Statistical Association · doi:10.1080/01621459.1988.10478560 · Cited by 2,311
Robust dynamic classes revealed by measuring the response function of a social system
Crane, R., & Sornette, D. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0803685105 · Cited by 786
On Lewis' simulation method for point processes
Ogata, Y. (1981) · IEEE Transactions on Information Theory · doi:10.1109/tit.1981.1056305 · Cited by 734
Vervaat, W. (1979) · Advances in Applied Probability · doi:10.1017/s0001867800033024 · Cited by 462
Predicting COVID-19 Spread from Large-Scale Mobility Data
Schwabe, A., Persson, J., & Feuerriegel, S. (2021) · Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining · doi:10.1145/3447548.3467157 · Cited by 26
Metadata
- Authors
- Hawkes, A. G., & Oakes, D.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1974-09
- Volume
- 11
- Issue
- 03
- Pages
- 493-503
- ISSN
- 0021-9002 (ISSN-L)
- 1475-6072
- OpenAlex
- W2328875713
- Cited by
- 757
- References
- 0
- FWCI
- 5.83
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A cluster process representation of a self-exciting process. https://app.cochat.ai/papers/10.1017/s0021900200096273
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- Hawkes, A. G., & Oakes, D. (1974). A cluster process representation of a self-exciting process. Journal of Applied Probability. https://doi.org/10.1017/s0021900200096273
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
