DOI

For a Borel set A and a homogeneous Poisson point process λ in Rd of intensity λ > 0, define the Poisson-Voronoi approximation Aλ of A as a union of all Voronoi cells with nuclei from λ lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AδAη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AδAη) together with their asymptotics for large λ are obtained as well. © Applied Probability Trust 2012.
Original languageEnglish
Pages (from-to)938-953
Number of pages16
JournalAdvances in Applied Probability
Volume44
Issue number4
DOIs
StatePublished - 1 Dec 2012

    Research areas

  • Perimeter, Poisson point process, Poisson-Voronoi cell, Poisson-Voronoi tessellation

ID: 126290227