Related papers: On total claim amount for marked Poisson cluster m…
Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of…
We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…
This paper investigates the form of optimal reinsurance contracts in the case of clusters of losses. The underlying insured risk is represented by a marked Hawkes process, where the intensity of the jumps depends not only on the occurrence…
We consider the problem of estimating the number of types in a corpus using the number of types observed in a sample of tokens from that corpus. We derive exact and asymptotic distributions for the number of observed types, conditioned upon…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
In actuarial practice, the usual independence assumptions for the collective risk model are often violated, implying a growing need for considering more general models that incorporate dependence. To this purpose, the present paper studies…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
Contemporary insurance theory is concentrated on models with different types of polices and shock events may influence the payments on some of them. Jordanova (2018) considered a model where a shock event contributes to the total claim…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic \chi^2-goodness-of-fit test.…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…
In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without…
A $U$-statistic of a Poisson point process is defined as the sum $\sum f(x_1,\ldots,x_k)$ over all (possibly infinitely many) $k$-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-It\^{o} chaos…
We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…