## LIMIT THEOREMS FOR ITERATION STABLE TESSELLATIONS

Autor(en): | Schreiber, Tomasz Thaele, Christoph |

Stichwörter: | 2ND-ORDER PROPERTIES; CELLS; Central limit theorem; CONSTRUCTION; functional limit theorem; iteration/nesting; Markov process; martingale theory; Mathematics; random tessellation; STATIONARY; Statistics & Probability; stochastic geometry; stochastic stability |

Erscheinungsdatum: | 2013 |

Herausgeber: | INST MATHEMATICAL STATISTICS |

Journal: | ANNALS OF PROBABILITY |

Volumen: | 41 |

Ausgabe: | 3B |

Startseite: | 2261 |

Seitenende: | 2278 |

Zusammenfassung: | The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in R-d, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment process induced a by STIT tessellation relative to an initial time moment is shown. As second main result, a central limit theorem for the total edge length/facet surface is obtained, with a normal limit distribution in the planar case and, most interestingly, with a nonnormal limit showing up in all higher space dimensions. |

ISSN: | 00911798 |

DOI: | 10.1214/11-AOP718 |

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