Year: 2020
Type: preprint
Abstract: This work contributes to the theory and applications of Hawkes processes. We introduce and examine a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass -- the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for explicit modelling of simultaneous occurrence of excitation events coming from different sources, i.e. caused by different coordinates of the multivariate process. We study the issue of existence of a generalized Hawkes process, and we provide a construction of a specific generalized multivariate Hawkes process. We investigate Markovian aspects of GMHPs, and we indicate some plausible important applications of GMHPs.
Source: arXiv (Cornell University)
Institutions: Illinois Institute of Technology, University of Warsaw
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286793343