Second-order theory for iteration stable tessellations

• Autorzy: Schreiber T. , Thäle C.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible family of space-time models considered in stochastic geometry. The previously developed martingale tools are used to study second-order properties of STIT tessellations. A general formula for the variance of the total surface area of cell boundaries inside an observation window is shown. This general expression is combined with tools from integral geometry to derive exact and asymptotic second-order formulas in the stationary and isotropic regime. Also a general formula for the pair-correlation function of the surface measure is found.

Słowa kluczowe

EN

chord-power integral; integral geometry; iteration/nesting; martingale theory; pair correlation function; random geometry; random tessellation; stochastic stability; stochastic geometry

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2012
• Tom: Vol. 32, Fasc. 2
• Strony: 281--300
• Opis fizyczny: Bibliogr. 21 poz., rys., wykr.

Twórcy

autor

Schreiber T.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

autor

Thäle C.

• Institute for Mathematics, University of Osnabrück, Albrechtstraße 28a, D-49088 Osnabrück, Germany
• Faculty of Mathematics, Ruhr-University Bochum, NA 3/68, D-44780 Bochum, Germany

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