Original scientific paper

On the Bartlett spectrum of randomized Hawkes processes

Mark Kelbert ; Department of Mathematics, University of Wales-Swansea, Singleton Park, Swansea, UK
Nikolai Leonenko ; Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, UK
Vladimir Belitsky ; IME, University of Sao Paulo, Sao Paulo, Brazil

Abstract

We study the Bartlett spectrum of the randomized Hawkes process and demonstrate that it behaves very differently from the case of a classical Hawkes process. In particular, the Bartlett spectrum could have a singularity near the origin which indicates a long-range dependence property.

Keywords

point process; Hawkes process; randomization; Bartlett spectrum; long-range dependence; Mittag-Lefler function

Hrčak ID:

110832

URI

https://hrcak.srce.hr/110832

Publication date:

19.11.2013.

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