Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
Xuefeng Gao () and
Lingjiong Zhu ()
Additional contact information
Xuefeng Gao: The Chinese University of Hong Kong
Lingjiong Zhu: Florida State University
Queueing Systems: Theory and Applications, 2018, vol. 90, issue 1, No 6, 206 pages
Abstract A univariate Hawkes process is a simple point process that is self-exciting and has a clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history of the point process. Hawkes processes have wide applications in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we prove a functional central limit theorem for stationary Hawkes processes in the asymptotic regime where the baseline intensity is large. The limit is a non-Markovian Gaussian process with dependent increments. We use the resulting approximation to study an infinite-server queue with high-volume Hawkes traffic. We show that the queue length process can be approximated by a Gaussian process, for which we compute explicitly the covariance function and the steady-state distribution. We also extend our results to multivariate stationary Hawkes processes and establish limit theorems for infinite-server queues with multivariate Hawkes traffic.
Keywords: Stationary Hawkes processes; Functional central limit theorem; Infinite-server queues; Gaussian limits; 60F17; 60K25; 90B22 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s11134-018-9570-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:queues:v:90:y:2018:i:1:d:10.1007_s11134-018-9570-5
Ordering information: This journal article can be ordered from
Access Statistics for this article
Queueing Systems: Theory and Applications is currently edited by Sergey Foss
More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla ().