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Stochastic geometry.

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Stochastic geometry. --- Mathematical physics. --- Physical mathematics --- Physics --- Geometry --- Mathematics

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This book deals with the Boolean model, a basic model of stochastic geometry for the description of porous structures like the pore space in sand stone. The main result is a formula which gives in two and three dimensions a series representation of the most important model parameter, the intensity, using densities of so-called harmonic intrinsic volumes, which are new observable geometric quantities.

Stochastic geometry --- Boolean model --- Intensitätsschätzung --- method of densities --- anisotropy --- Anisotropie --- intensity estimation --- Boolesches Modell --- Stochastische Geometrie

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This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in Hörmander's form, by using the connection between stochastic flows and partial differential equations. The book stresses the author's view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughou

Stochastic geometry. --- Flows (Differentiable dynamical systems) --- Stochastic differential equations. --- Differentiable dynamical systems --- Differential equations --- Fokker-Planck equation --- Geometry --- Equations différentielles stochastiques --- Géométrie stochastique

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Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer school in Martina Franca in September 1974. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry.

Stochastic geometry --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematics. --- Math --- Convex geometry. --- Discrete geometry. --- Differential geometry. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Convex and Discrete Geometry. --- Differential Geometry. --- Science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Geometry --- Combinatorial geometry --- Distribution (Probability theory. --- Discrete groups. --- Global differential geometry. --- Geometry, Differential --- Groups, Discrete --- Infinite groups --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Discrete mathematics --- Convex geometry . --- Distribution. --- Stochastic geometry - Congresses