相关论文: Factorial moments of point processes

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by the event-by-event analysis in relativistic heavy-ion collisions. After defining the factorial cumulants for…

Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains.…

In recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point…

We compute the moment of order n of the Poisson stochastic integral of a random process u over a metric space X as a sum that runs over all partitions of {1,...,n} and involves the addition of points to Poisson configurations. This formula…

We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…

We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random…

We propose to verify relations between quantities which characterize scaling properties of high energy density fluctuations in terms of factorial moments and newly introduced associated frequency moments. Typical examples are presented in…

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…

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…

Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…

We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…

Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…

The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…

We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…

Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…

Recently the identity method was proposed to calculate second moments of the multiplicity distributions from event-by-event measurements in the presence of the effects of incomplete particle identification. In this paper the method is…