Multivariate Generalized Hawkes Processes

A very interesting class of stochastic processes was introduced in 1971 by Alan Hawkes. These processes, called now Hawkes processes, are meant to model self-exciting and mutually-exciting random phenomena that evolve in time. The self-exciting phenomena are modeled as univariate Hawkes processes, and the mutually-exciting phenomena are modeled as multivariate Hawkes processes. Hawkes processes belong to the family of marked point processes, and, of course, a univariate Hawkes process is just a special case of the multivariate one.

In this talk I will discuss generalized multivariate Hawkes processes, as well as the related Hawkes structures. Generalized multivariate Hawkes processes 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. The importance of this feature is rather intuitive, and it will be illustrated by some examples.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning