Communications in Information and Systems

Volume 21 (2021)

Number 3

Hawkes processes: some key ideas, links to neuroscience and system identification

Pages: 385 – 413

DOI: https://dx.doi.org/10.4310/CIS.2021.v21.n3.a4

Authors

László Gerencsér (Institute for Computer Science and Control (SZTAKI), Eötvös Loránd Research Network (ELKH), Budapest, Hungary; and Széchenyi István University, Győr, Hungary)

György Perczel (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University (PPKE ITK), Budapest, Hungary; and Széchenyi István University, Győr, Hungary)

Loránd Erőss (National Institute of Clinical Neurosciences (OKITI), Budapest, Hungary; and Faculty of Information Technology and Bionics, Pázmány Péter Catholic University (PPKE ITK), Budapest, Hungary)

Dániel Fabó (National Institute of Clinical Neurosciences (OKITI), Budapest, Hungary; and Faculty of Information Technology and Bionics, Pázmány Péter Catholic University (PPKE ITK), Budapest, Hungary)

Zsuzsanna Vágó (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University (PPKE ITK), Budapest, Hungary; and Széchenyi István University, Győr, Hungary)

Abstract

The primary objective of the present paper is to provide a brief survey of basic ideas and some key results of the theory of Hawkes processes that may serve as an interface for multidisciplinary research between mathematics and neurosciences, with hints to epidemiology. The class of Hawkes processes is considered as an appropriate model to describe the pattern of neuronal firing, see [56] [38]. As such, it is a prime candidate for detecting changes in brain activity, and consequently to predict epileptic seizures. Most of the advanced results will be presented via simple examples. In addition, we elaborate on links between the theory of Hawkes processes and linear stochastic systems, in particular system identification. A few new results in this context will be also presented with the outline of their proofs.

Full Text (PDF format)

This research was partially supported by the National Research, Development and Innovation Office of Hungary, Grant no: EFOP-3.6.2.-16-2017-00015, title: “Extending the Hungarian Service Network for Mathematics in Industry and Innovations”, and by its Autonomous Systems National Laboratory Program.

Received 30 September 2020

Published 4 June 2021