Related papers: Mixing of Poisson random measures under interactin…

We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe…

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…

In this note we consider the perfect integrator driven by Poisson process input. We derive its equilibrium and response properties and contrast them to the approximations obtained by applying the diffusion approximation. In particular, the…

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…

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our…

Let X be a Poisson point process of intensity lambda on the real line. A thickening of it is a (deterministic) measurable function f such that the union of X and f(X) is a Poisson point process of intensity lambda' where lambda'>lambda. An…

In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…

It is proved that the Poisson measure is a spectral measure of some family of commuting selfadjoint operators acting on a space constructed from some generalization of the moment problem.

It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…

This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward…

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…

This paper will be devoted to study weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will…

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…

We study systems of simple point processes that admit stochastic intensities. We represent these point processes as thinnings of Poisson measures and are interested in a convergence result of such systems. This result states that, if the…

While on the one hand, chaotic dynamical systems can be predicted for all time given exact knowledge of an initial state, they are also in many cases rapidly mixing, meaning that smooth probabilistic information (quantified by measures) on…

Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…