Related papers: Population viewpoint on Hawkes processes

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…

We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each…

This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…

The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its…

We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability…

This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…

Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they…

Hawkes Processes are a type of point process which models self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis.Recently, a…

A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed…

In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process, the Age Dependent Hawkes process, which…

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…

We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…

In this paper, we use a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and contact with the environment. Our aim is to estimate the…

By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…

Among the statistical tools for online information diffusion modeling, both epidemic models and Hawkes point processes are popular choices. The former originate from epidemiology, and consider information as a viral contagion which spreads…

We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a…

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. [arXiv:2208.07340] considering a finite population stratified by age bands. We model the actual unobserved infections using a latent marked…