Related papers: Spatiotemporal Hawkes processes with a graphon-ind…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
The Hawkes process is a simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous-time setting. However, data is also recorded in a…
Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban…
Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and…
In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model is characterized to allow these parameters to take negative…
We consider translation-invariant, finite range, supercritical contact processes. We show the existence of unbounded space-time cones within which the descendancy of the process from full occupancy may with positive probability be identical…
Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…
Effective investment planning decisions are crucial to ensure cyber-physical infrastructures satisfy performance requirements over an extended time horizon. Computing these decisions often requires solving Capacity Expansion Problems…
We provide an iterative solution approach for the indefinite Helmholtz equation discretised using finite elements, based upon a Hermitian Skew-Hermitian Splitting (HSS) iteration applied to the shifted operator, and prove that the iteration…
We study an iterated temporal and contemporaneous aggregation of $N$ independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index $\alpha \in (0, 2)$. Limits of…
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…
We consider a discrete-time version of a Hawkes process defined as a Poisson auto-regressive process whose parameters depend on the past of the trajectory. We allow these parameters to take on negative values, modelling inhibition. More…
Recent developments in ``Einstein Dehn filling'' allow the construction of infinitely many Einstein manifolds that have different topologies but are geometrically close to each other. Using these results, we show that for many spatial…
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…
We consider marked point processes on the d-dimensional euclidean space, defined in terms of a quasilocal specification based on marked Poisson point processes. We investigate the possibility of constructing absolutely-summable Hamiltonians…
Hawkes processes are point processes with self-exciting and clustering properties that are popular in applications. In recent years, renewal Hawkes processes have gained attention, due to their versatility such as the capability of…
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other…
Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual…
We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…