Criteria for Poisson process convergence with applications to inhomogeneous Poisson–Voronoi tessellations

This article employs the relation between probabilities of two consecutive values a Poisson random variable to derive conditions for weak convergence point processes process. As applications, we consider starting points k -runs in sequence Bernoulli variables, constructed using inradii and circumscribed radii inhomogeneous Poisson–Voronoi tessellations large nearest neighbor distances Boolean model disks.