Ratio limits and simulation algorithms for the Palm version of stationary iterated tessellations
نویسندگان
چکیده
Distributional properties and a simulation algorithm for the Palm version of stationary iterated tessellations are considered. In particular we study the limit behavior of functionals related to Cox-Voronoi cells (such as typical shortest path lengths) if either the intensity γ0 of the initial tessellation or the intensity γ1 of the component tessellation converges to 0. We develop an explicit description of the Palm version of Poisson-Delaunay tessellations (PDT) which provides a new direct simulation algorithm for the typical Cox-Voronoi cell based on PDT. It allows us to simulate the Palm version of stationary iterated tessellations where either the initial or component tessellation is a PDT and can furthermore be used in order to show numerically that the qualitative and quantitative behavior of certain functionals related to Cox-Voronoi cells strongly depends on the type of the underlying iterated tessellation.
منابع مشابه
Distributional properties of the typical cell of stationary iterated tessellations
Distributional properties are considered of the typical cell of stationary iterated tessellations (SIT), which are generated by stationary Poisson-Voronoi tessellations (SPVT) and stationary Poisson line tessellations (SPLT), respectively. Using Neveu’s exchange formula, the typical cell of SIT can be represented by those cells of its component tessellation hitting the typical cell of its initi...
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