Related papers: On multivariate modifications of Cramer Lundberg r…

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…

We study a generalization of the model introduced by Kistler and Schmidt in $2015$, that interpolates between the random energy model (REM) and the branching random walk (BRW). More precisely, we are interested in the asymptotic behaviour…

The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…

We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

Event of the same type occurring several times for one individual (recurrent events) are present in various domains (industrial systems reliability, episodes of unemployment, political conflicts, chronic diseases episodes). Analysis of such…

Most of the banks' operational risk internal models are based on loss pooling in risk and business line categories. The parameters and outputs of operational risk models are sensitive to the pooling of the data and the choice of the risk…

We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…

We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point…

Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…

An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic…

It is usual to consider data protection and learnability as conflicting objectives. This is not always the case: we show how to jointly control inference --- seen as the attack --- and learnability by a noise-free process that mixes…

We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…

A compound Poisson process whose jump measure and intensity are unknown is observed at finitely many equispaced times. We construct a purely data-driven estimator of the L\'evy density $\nu$ through the spectral approach using general…

This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…

Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$…

We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of…

We study the default risk in incomplete information. That means, we model the value of a firm by one L\'evy process which is the sum of brownian motion with drift and compound Poisson process. This L\'evy process can not be observed…