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We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We prove quantitative homogenization results for harmonic functions on supercritical continuum percolation clusters--that is, Poisson point clouds with edges connecting points which are closer than some fixed distance. We show that, on…
We describe a set of new estimators for the N-point correlation functions of point processes. The variance of these estimators is calculated for the Poisson and binomial cases. It is shown that the variance of the unbiased estimator…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
The Ginibre point process is one of the main examples of deter- minantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in pratical applications. However, this model has mostly been…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bound for the approximation error, which is of order 1/N in…
Based on Stein's method, we derive upper bounds for Poisson process approximation in the $L_1$-Wasserstein metric $d_2^{(p)}$, which is based on a slightly adapted $L_p$-Wasserstein metric between point measures. For the case $p=1$, this…
We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…
Keeler, Ross and Xia (2016) recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
We use Stein's method to provide non asymptotic $L^1$ bounds to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and $\alpha$-mixing properties that was recently…
In this paper, we study two specific types of $d$-dimensional Poisson functionals: a double-sum type and a sum-log-sum type, both over pairs of Poisson points. On these functionals, we impose column-type dependence, i.e., local behavior in…
Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used…
We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of a Gibbs point process interacting via a finite-range stable potential. This result holds for all activities $\lambda$ for which the…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…