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Cumulants of Hawkes point processes
KTH, School of Computer Science and Communication (CSC).
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, no 4, 042802Article in journal (Refereed) Published
Abstract [en]

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible "family trees," representing complex interactions between point events. We also consider the problem of computing the integrated cumulants, characterizing the average measure of correlated activity between events of different types, and derive the relevant equations.

Place, publisher, year, edition, pages
2015. Vol. 91, no 4, 042802
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Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-166489DOI: 10.1103/PhysRevE.91.042802ISI: 000352259200009OAI: oai:DiVA.org:kth-166489DiVA: diva2:812338
Note

QC 20150518

Available from: 2015-05-18 Created: 2015-05-11 Last updated: 2017-12-04Bibliographically approved

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Jovanovic, StojanHertz, John
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School of Computer Science and Communication (CSC)Nordic Institute for Theoretical Physics NORDITA
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