Related papers: Factorial moments of point processes
We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained…
We establish asymptotic formulae for general joint moments of characteristic polynomials and their higher-order derivatives associated with matrices drawn randomly from the groups $\mathrm{USp}(2N)$ and $\mathrm{SO}(2N)$ in the limit as…
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero…
It has been demonstrated that factorial moments analysis in dependence from the size of phase-space cells (when the latter is decreased but is still considerably large), exhibits sensitivity to particle bunching within a system situated in…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…
Shot-noise and fractional Poisson processes are instances of filtered Poisson processes. We here prove Girsanov theorem for this kind of processes and give an application to an estimate problem.
In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between…
We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our…
In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension $d$ at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., an equivariant measurable function of…
Process monitoring and control requires detection of structural changes in a data stream in real time. This article introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function, and establish several central limit…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
We discuss the equivalence of definitions for conditional Poisson processes, Cox processes, and stochastic intensities of point processes on the real line. We show that Watanabe's characterisation of conditional Poisson processes in terms…
In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…
A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Given a Poisson process on a $d$-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the \u{C}ech complex associated to the coverage of…
If you take a superposition of n IID copies of a point process and thin that by a factor of 1/n, then the resulting process tends to a Poisson point process as n tends to infinity. We give a simple proof of this result that highlights its…