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The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.

Stochastic geometry --- Factorization (Mathematics) --- Geometric probabilities --- 519.21 --- Geometry --- Probabilities --- Mathematics --- Probability theory. Stochastic processes --- Geometric probabilities. --- Stochastic geometry. --- Factorization (Mathematics). --- 519.21 Probability theory. Stochastic processes

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This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists.

Stochastic processes --- Discrete mathematics --- Combinatorial probabilities --- Stochastic geometry --- Mathematical optimization --- Random graphs --- Mathematical Statistics --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Combinatorial optimization --- Combinatorische optimisatie --- Optimalisation combinatoire --- Probabiliteit--Theorie --- Probabiliteitstheorie --- Probabilities --- Probabilité [Théorie de la ] --- Probabilités --- Waarschijnlijkheid--Theorie --- Waarschijnlijkheidstheorie --- Geometry. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Euclid's Elements

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Probability theory --- Stochastic analysis --- Analyse stochastique --- Davidson, Rollo, --- Davidson, Rollo --- 519.216 --- #WWIS:STAT --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Festschrift - Libri Amicorum --- Stochastic analysis. --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic geometry --- Géométrie stochastique. --- Processus stochastiques --- Probabilités. --- Probabilities --- Géométrie stochastique. --- Probabilités