A Mecke-type formula and Markov properties for STIT tessellation processes

Werner Nagel; Linh Ngoc Nguyen; Christoph Thaele; Viola Weiss

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arXiv · 1612.03078

A Mecke-type formula and Markov properties for STIT tessellation processes

Werner Nagel·Linh Ngoc Nguyen·Christoph Thaele·Viola Weiss

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Abstract

An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property of a class of associated random processes is derived. This in turn is used to determine the distribution of the number of internal vertices of the typical maximal tessellation segment.

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Werner Nagel, Linh Ngoc Nguyen, Christoph Thaele, Viola Weiss. 2016-12-09. A Mecke-type formula and Markov properties for STIT tessellation processes. https://arxiv.org/abs/1612.03078

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