6 papers · 1 filter
Geometric BSDEs
Roger J. A. Laeven, Emanuela Rosazza Gianin, Marco Zullino
We introduce Geometric Backward Stochastic Differential Equations (GBSDEs) and two-driver BSDEs, which arise naturally in the geometric dynamics of dynamic return risk measures and…
Markovian multivariate Hawkes population processes: Efficient evaluation of moments
R. S. Karim, R. J. A. Laeven, M +1
We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in…
Delayed Hawkes birth-death processes
Justin Baars, Roger J. A. Laeven, Michel Mandjes
We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not incre…
Sample Path Large Deviations for Multivariate Heavy-Tailed Hawkes Processes and Related Lévy Processes
Jose Blanchet, Roger J. A. Laeven, Xingyu Wang +1
In this paper, we develop sample path large deviations for multivariate Hawkes processes with heavy-tailed mutual excitation rates. Our results address a broad class of rare events…
Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes
Jose Blanchet, Roger J. A. Laeven, Xingyu Wang +1
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes.…
Spatiotemporal Hawkes processes with a graphon-induced connectivity structure
Justin Baars, Roger J. A. Laeven, Michel Mandjes
We introduce a spatiotemporal self-exciting point process , boundedly finite both over time and space , with excitation structure determined by a…