Communications in Information and Systems
Volume 21 (2021)
Hawkes processes: some key ideas, links to neuroscience and system identification
Pages: 385 – 413
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  . 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.
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