Related papers: Quasi-likelihood analysis for marked point process…
This paper tackles the issue of establishing a lower-bound on the asymptotic ratio of survival probabilities between two different initial conditions, asymptotically in time for a given Markov process with extinction. Such a comparison is a…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag-Leffler distribution. This is the generalization of the work presented in [10]. We derive analytical results for the…
A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a model for the data generating mechanism. This paper focuses on a Bayesian…
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…
Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly…
The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future…
Hawkes process is a simple point process 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, social networks,…
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…
The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against…
The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…
We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In…
Hawkes process are very popular mathematical tools for modelling phenomena exhibiting a \textit{self-exciting} or \textit{self-correcting} behaviour. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime…