Introduction To Geometric Probability

Author : Daniel A. Klain
Publisher : Cambridge University Press
ISBN 13 : 9780521596541
Total Pages : 196 pages
Book Rating : 4.48/5 ( download)

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Download or read book Introduction to Geometric Probability written by Daniel A. Klain and published by Cambridge University Press. This book was released on 1997-12-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santal and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove the fundamental theorem of integral geometry, namely, the kinematic formula. Finally, the analogies between invariant measures on polyconvex sets and measures on order ideals of finite partially ordered sets are investigated. The relationship between convex geometry and enumerative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems.

Author : A.M. Mathai
Publisher : CRC Press
ISBN 13 : 9789056996819
Total Pages : 580 pages
Book Rating : 4.19/5 ( download)

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Download or read book An Introduction to Geometrical Probability written by A.M. Mathai and published by CRC Press. This book was released on 1999-12-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.

Author : Herbert Solomon
Publisher : SIAM
ISBN 13 : 0898710251
Total Pages : 180 pages
Book Rating : 4.50/5 ( download)

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Download or read book Geometric Probability written by Herbert Solomon and published by SIAM. This book was released on 1978-06-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; and much more.

Author : Rolf Schneider
Publisher : Springer Science & Business Media
ISBN 13 : 354078859X
Total Pages : 692 pages
Book Rating : 4.91/5 ( download)

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Download or read book Stochastic and Integral Geometry written by Rolf Schneider and published by Springer Science & Business Media. This book was released on 2008-09-08 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Henry C. Tuckwell
Publisher : Routledge
ISBN 13 : 1351452959
Total Pages : 200 pages
Book Rating : 4.53/5 ( download)

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Download or read book Elementary Applications of Probability Theory written by Henry C. Tuckwell and published by Routledge. This book was released on 2018-02-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.

Author : John E. Freund
Publisher : Courier Corporation
ISBN 13 : 0486158438
Total Pages : 247 pages
Book Rating : 4.33/5 ( download)

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Download or read book Introduction to Probability written by John E. Freund and published by Courier Corporation. This book was released on 2012-05-11 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. Exercises with some solutions. Summary. 1973 edition.

Author : Geoffrey Grimmett
Publisher : Oxford University Press, USA
ISBN 13 : 0198709978
Total Pages : 281 pages
Book Rating : 4.78/5 ( download)

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Download or read book Probability written by Geoffrey Grimmett and published by Oxford University Press, USA. This book was released on 2014 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

Author : Ronald Meester
Publisher : Birkhäuser
ISBN 13 : 3034877862
Total Pages : 196 pages
Book Rating : 4.62/5 ( download)

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Download or read book A Natural Introduction to Probability Theory written by Ronald Meester and published by Birkhäuser. This book was released on 2013-03-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compactly written, but nevertheless very readable, appealing to intuition, this introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Technical machinery is only introduced when necessary. The route is rigorous but does not use measure theory. The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory. Only first-year calculus is required.

Author : Evgeny Spodarev
Publisher : Springer
ISBN 13 : 3642333052
Total Pages : 446 pages
Book Rating : 4.57/5 ( download)

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Download or read book Stochastic Geometry, Spatial Statistics and Random Fields written by Evgeny Spodarev and published by Springer. This book was released on 2013-02-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Author : Geoffrey Grimmett
Publisher : Oxford University Press
ISBN 13 : 9780198532644
Total Pages : 230 pages
Book Rating : 4.44/5 ( download)

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Download or read book Probability written by Geoffrey Grimmett and published by Oxford University Press. This book was released on 1986 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to probability and random processes at first-degree level with exercises and problems.