Description
Springer Stochastic And Integral Geometry 2008 Edition by Rolf Schneider Wolfgang Weil
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions and it has vigorously developed during recent decades when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is therefore the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry - random sets point processes random mosaics - and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included and much additional information is given in the section notes. Table of contents : Foundations of Stochastic Geometry.- Prolog.- Random Closed Sets.- Point Processes.- Geometric Models.- Integral Geometry.- Averaging with Invariant Measures.- Extended Concepts of Integral Geometry.- Integral Geometric Transformations.- Selected Topics from Stochastic Geometry.- Some Geometric Probability Problems.- Mean Values for Random Sets.- Random Mosaics.- Non-stationary Models.- Facts from General Topology.- Invariant Measures.- Facts from Convex Geometry.