Related papers: On a generalization of Mat\'ern hard-core processe…
Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric settings, such as when inputs lie on a Riemannian manifold,…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…
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…
Poisson thinning is an elementary result in probability, which is of great importance in the theory of Poisson point processes. In this article, we record a couple of characterization results on Poisson thinning. We also consider several…
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…
We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two…
Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We…
We study the binary classification problem for Poisson point processes, which are allowed to take values in a general metric space. The problem is tackled in two different ways: estimating nonparametricaly the intensity functions of the…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
We study finite horizon optimal switching problems for hidden Markov chain models under partially observable Poisson processes. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state…
With nuclear targets comes a new scale into the pQCD description of hard processes - the saturation scale. In the saturation regime, the familiar linear k_\perp-factorization breaks down and must be replaced by a nonlinear…
Consider the point process (in $\mathbb{R}^d$) of local maxima of smooth Gaussian fields, with sufficient decay of correlation at infinity, above a level $u$. We show that this point process, rescaled appropriately, converges weakly to a…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
We show that the splitting-characterization of the Poisson point process is an immediate consequence of the Mecke-formula.