Related papers: Population viewpoint on Hawkes processes
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…
We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…
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, insurance, neuroscience,…
In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…
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…
Gun violence and mass shootings are high-profile epidemiological issues facing the United States with questions regarding their contagiousness gaining prevalence in news media. Through the use of nonparametric Hawkes processes, we examine…
The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or non-stationary ones. We also study the branching random walk on $Z^d$ with immigration…
We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we present a full kinetic framework for age-structured interacting populations undergoing birth, death and…
We consider a class of Crump-Mode-Jagers processes with interaction, constructed by removing a newly born offspring with a probability that depends on the age structure of the population at its birth time. We prove a law of large numbers…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…
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 increase at arrivals but at departures from the system. In a…
We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result…
The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations…
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…
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the…