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Cumulants of Hawkes point processes
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Copenhagen, Denmark.
Number of Authors: 32015 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 91, no 4, article id 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, article id 042802
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Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-159589DOI: 10.1103/PhysRevE.91.042802ISI: 000352259200009PubMedID: 25974542OAI: oai:DiVA.org:su-159589DiVA, id: diva2:1245122
Available from: 2018-09-04 Created: 2018-09-04 Last updated: 2018-09-04Bibliographically approved

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