A Mecke-type formula and Markov properties for STIT tessellation   processes
  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. 
Werner Nagel, Linh Ngoc Nguyen, Christoph Thaele, Viola Weiss
math.PR