94 citations · 161 across the 8 of their papers we have counts for
5 papers · 1 filter
Loglinear Hawkes processes: existence, nonexplosion, stability and moment bounds
Tomasz R. Bielecki, Jacek Jakubowski, Matthias Kirchner +1
This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. Such pr…
Critical cluster cascades
Matthias Kirchner
We consider a sequence of Poisson cluster point processes on : at step of the construction, the cluster centers have intensity for some $…
A note on critical Hawkes processes
Matthias Kirchner
Let be a distribution function on with and density . Let be the distribution function of , .…
Hawkes and INAR() processes
Matthias Kirchner
In this paper, we discuss integer-valued autoregressive time series (INAR), Hawkes point processes, and their interrelationship. Besides presenting structural analogies, we derive…
An estimation procedure for the Hawkes process
Matthias Kirchner
In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the num…