Cumulants of Hawkes point processes
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
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
IdentifiersURN: urn:nbn:se:kth:diva-166489DOI: 10.1103/PhysRevE.91.042802ISI: 000352259200009OAI: oai:DiVA.org:kth-166489DiVA: diva2:812338
QC 201505182015-05-182015-05-112015-05-18Bibliographically approved