2011/06/01 by Eike Biehler, Biehler, Eike
Mathematics · #60D05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60D05
paper · pdf · doi:10.48550/arxiv.1106.0105
25 pages
arxiv created 2011/06/01 · arxiv updated 2011/06/02
The STIT tessellation process was introduced and examined by Mecke, Nagel and Weiß; many of its main characteristics are contained in a paper published by Nagel and Weiß in 2005. In a paper published in 2010, Mecke introduced another process in discrete time. With a geometric distribution whose parameter depends on the time, he reaches a continuous-time model. In his Conjecture 3, he assumed this continuous-time model to be equivalent to STIT. In the present paper, that conjecture is proven. An interesting relation arises to a continuous-time version of the equally-likely model classified by Cowan in 2010. This will also clarify how Mecke's model works as a process in continuous time.