Related papers: Testing the first-order separability hypothesis fo…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is…
In a spatial-temporal model, structural change and/or spatial heterogeneity can easily affect estimation of parameters. Following the spatial-temporal model in [1], we develop a nonparametric procedure for test-ing the presence of…
In the realm of large-scale spatiotemporal data, abrupt changes are commonly occurring across both spatial and temporal domains. This study aims to address the concurrent challenges of detecting change points and identifying spatial…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
We construct a modification of the Poisson bracket which is suitable for a canonical analysis of space-time noncommutative field theories. We show that this bracket satisfies the Jacobi identities and generates equations of motion. In this…
We study conditions so that the determinantal point process $\Lambda_\phi$ associated to a generalized Fock space defined by a doubling subharmonic weight $\phi$ is almost surely a separated sequence in $\mathbb C$. Under a natural…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We propose a nonparametric test of spatial independence for data observed on irregular, non-lattice point clouds $\mathcal{V}_{n}\subset\mathbb{R}^{2}$. For each location $v\in\mathcal{V}_{n}$, we encode the local spatial configuration…
Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons,…
The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct…
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
We study the rate of convergence in the Shape Theorem of first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are stated for a given…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…