Related papers: A tutorial on Palm distributions for spatial point…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…
We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the…
The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class of such stationary…
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from…
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals.…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
We discuss certain renormalised first passage bridges of self-similar processes. These processes generalise the Brownian co-ascent, a term recently introduced by H. Panzo (S\'eminaire de Probabilit\'es L, 2019). Our main result states that…
Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation…
The goal of the article is to develop the approach of substationarity to spatial point processes (SPPs). Substationarity is a new concept, which has never been studied in the literature. It means that the distribution of SPPs can only be…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
We propose PALPS, a Process Algebra with Locations for Population Systems. PALPS allows us to produce spatially-explicit, individual-based models and to reason about their behavior. Our calculus has two levels: at the first level we may…