Related papers: Convergences for a Virus-like Evolving Population …
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…
We introduce a new type of point process model to describe the incidence of contagious diseases. The model is a variant of the Hawkes self-exciting process and exhibits similar clustering but without the restriction that the component…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events.…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the…
The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
In this article, we consider time-changed models of population evolution $\mathcal{X}^f(t)=\mathcal{X}(H^f(t))$, where $\mathcal{X}$ is a counting process and $H^f$ is a subordinator with Laplace exponent $f$. In the case $\mathcal{X}$ is a…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the…
We analyse the stochastic comparison of interacting particle systems allowing for multiple arrivals, departures and non-conservative jumps of individuals between sites. That is, if $k$ individuals leave site $x$ for site $y$, a possibly…
Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work,…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a…
In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…