Stochastic and Integral Geometry
Title | Stochastic and Integral Geometry PDF eBook |
Author | Rolf Schneider |
Publisher | Springer Science & Business Media |
Pages | 692 |
Release | 2008-09-08 |
Genre | Mathematics |
ISBN | 354078859X |
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.
Stochastic and Integral Geometry
Title | Stochastic and Integral Geometry PDF eBook |
Author | R.V. Ambartzumian |
Publisher | Springer Science & Business Media |
Pages | 135 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 9400939213 |
Stochastic Geometry
Title | Stochastic Geometry PDF eBook |
Author | David Coupier |
Publisher | Springer |
Pages | 240 |
Release | 2019-04-09 |
Genre | Mathematics |
ISBN | 3030135470 |
This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.
Stochastic Geometry
Title | Stochastic Geometry PDF eBook |
Author | W. Weil |
Publisher | Springer |
Pages | 0 |
Release | 2006-10-27 |
Genre | Mathematics |
ISBN | 9783540381747 |
Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.
Stochastic Geometry
Title | Stochastic Geometry PDF eBook |
Author | W. Weil |
Publisher | Springer |
Pages | 302 |
Release | 2006-10-26 |
Genre | Mathematics |
ISBN | 3540381759 |
Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.
Stochastic Geometry
Title | Stochastic Geometry PDF eBook |
Author | Viktor Benes |
Publisher | Springer Science & Business Media |
Pages | 231 |
Release | 2007-05-08 |
Genre | Mathematics |
ISBN | 1402081030 |
Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand.
Stochastic Geometry
Title | Stochastic Geometry PDF eBook |
Author | Rollo Davidson |
Publisher | Wiley-Interscience |
Pages | 426 |
Release | 1974-04-08 |
Genre | Mathematics |
ISBN |