Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane

DOI10.1239/aap/1293113144zbMath1221.60008arXiv1004.2013OpenAlexW2964312708MaRDI QIDQ3074485

Tomasz Schreiber, Christoph Thäle

Publication date: 9 February 2011

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2013

zbMATH Keywords

Markov processstochastic stabilitymartingalecross correlationcovariance measure

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (15)

Spatial Stit Tessellations: Distributional Results for I-Segments ⋮ Splitting tessellations in spherical spaces ⋮ Second-order comparison of three fundamental tessellation models ⋮ Stit Tessellations have Trivial Tail σ-Algebra ⋮ On the arrangement of cells in planar STIT and Poisson line tessellations ⋮ Limit theorems for iteration stable tessellations ⋮ Second-order properties for planar Mondrian tessellations ⋮ Geometry of iteration stable tessellations: connection with Poisson hyperplanes ⋮ Arak-Clifford-Surgailis tessellations. Basic properties and variance of the total edge length ⋮ Shape-driven nested Markov tessellations ⋮ Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations ⋮ A Mecke-type formula and Markov properties for STIT tessellation processes ⋮ Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane ⋮ Life after life. Remembering Tomasz Schreiber ⋮ Branching random tessellations with interaction: a thermodynamic view

Cites Work

• Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane
• SECOND MOMENT MEASURE AND K-FUNCTION FOR PLANAR STIT TESSELLATIONS
• Stochastic and Integral Geometry
• Cross-Correlation Measures of Weighted Random Measures and Their Estimation
• Correlations between Planar Random Structures, with an Ecological Application
• An Introduction to the Theory of Point Processes
• Second‐order properties of the point process of nodes in a stationary Voronoi tessellation
• A global construction of homogeneous random planar tessellations that are stable under iteration
• Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration
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