Theory of nonstationary Hawkes processes

Neta Ravid Tannenbaum, Yoram Burak

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We expand the theory of Hawkes processes to the nonstationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time-dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and the pattern and statistics of the external inputs. We illustrate the correlation structure using several examples in which neural network dynamics are modeled as a Hawkes process. In particular, we focus on the interplay between internally and externally generated oscillations and their signatures in the spike and rate correlation functions.

Original languageAmerican English
Article number062314
JournalPhysical Review E
Volume96
Issue number6
DOIs
StatePublished - 26 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 American Physical Society.

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