Regenerative processes for Poisson zero polytopes. (29th November 2018)

• Record Type: Journal Article
• Authors: Martínez, Servet; Nagel, Werner
• Is Part Of: Advances in applied probability. Volume 50:Number 4(2018)
• Page Start: 1217
• Page End: 1226
• Publication Date: 2018-11-29
• Subjects: Stochastic geometry, -- random tessellation, -- Poisson hyperplane tessellation, -- STIT tessellation, -- zero polytope, -- Bernoulli flow, -- regenerative process; Primary 60D05, -- 60J25, -- 60J75, -- 37A25, -- 37A35; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.57
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: Let ( M t : t >0) be a Markov process of tessellations of ℝ ℓ, and let (𝒞 t : t >0) be the process of their zero cells (zero polytopes), which has the same distribution as the corresponding process for Poisson hyperplane tessellations. In the present paper we describe the stationary zero cell process ( a t 𝒞 a t : t ∈ℝ), a >1, in terms of some regenerative structure and we show that it is a Bernoulli flow. An important application is to STIT tessellation processes.