8 citations · 8 across the 5 of their papers we have counts for
10 papers · 1 filter
Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes
Carina Betken, Matthias Schulte, Christoph Thäle
This paper deals with the union set of a stationary Poisson process of cylinders in having an -dimensional base and an -dimensional direction space, where…
Poisson process approximation under stabilization and Palm coupling
Omer Bobrowski, Matthias Schulte, D. Yogeshwaran
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range o…
Poisson approximation with applications to stochastic geometry
Federico Pianoforte, Matthias Schulte
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides,…
Rates of multivariate normal approximation for statistics in geometric probability
Matthias Schulte, J. E. Yukich
We employ stabilization methods and second order Poincaré inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})…
Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations
Federico Pianoforte, Matthias Schulte
This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a…
Non-standard limits for a family of autoregressive stochastic sequences
Sergey Foss, Matthias Schulte
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoreg…