相关论文: Distributional Limits for the Symmetric Exclusion …

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…

We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…

We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state…

We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…

An almost ubiquitous assumption made in the stochastic-analytic study of the quality of service in cellular networks is Poisson distribution of base stations. It is usually justified by various irregularities in the real placement of base…

This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension…

We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in…

An analogue of Talagrand's convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring…

In this paper, we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical…

Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems…

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…

We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the…

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous…

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…