We present new Poisson process approximation results for stabilizing functionals of and binomial point processes. These are allowed to have an unbounded range interaction encompass many examples in stochastic geometry. Our bounds derived the Kantorovich–Rubinstein distance using generator approach Stein’s method. give different types While some our given terms coupling with its Palm version, ot...

Abstract In this paper, we consider the Poisson equation on a “long” domain which is Cartesian product of one-dimensional long interval with ( d − 1)-dimensional domain. The right-hand side assumed to have rank-1 tensor structure. We will present and compare methods construct approximations solution structure computational effort governed by only solving elliptic problems lower-dimensional doma...

We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics...