A random cell splitting scheme on the sphere

Christian Deuss, Julia Hörrmann and Christoph Thäle

Stochastic Processes and their Applications, 2017, vol. 127, issue 5, 1544-1564

Abstract: A random recursive cell splitting scheme of the 2-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large array of combinatorial and metric parameters of the induced splitting tessellations by means of martingale methods combined with tools from spherical integral geometry. The findings are compared with those in the Euclidean case, making thereby transparent the influence of the curvature of the underlying space. Moreover, the capacity functional is computed and the point process that arises from the intersection of a splitting tessellation with a fixed great circle is characterized.

Keywords: Capacity functionals; Markov processes; Martingales; Palm distributions; Point processes; Random polygons; Random tessellations; Spherical intrinsic volumes; Spherical spaces; Spherical stochastic geometry (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414915301290
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:5:p:1544-1564

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2016.08.010

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().