Stochastic Geometry

Author : Dietrich Stoyan,Wilfrid S. Kendall
Publisher : Wiley
Page : 458 pages
File Size : 41,7 Mb
Release : 2009-03-16
Category : Mathematics
ISBN : 0470743646

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Stochastic Geometry and its Applications by Dietrich Stoyan,Wilfrid S. Kendall Pdf

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The book deals with the following topics: point processes random sets random measures random shapes fibre and surface processes tessellations stereological methods. This book has served as the key reference in its field for over 20 years and is regarded as the best treatment of the subject of stochastic geometry, both as an subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right.

Author : David Coupier
Publisher : Springer
Page : 232 pages
File Size : 42,8 Mb
Release : 2019-04-09
Category : Mathematics
ISBN : 9783030135478

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Stochastic Geometry by David Coupier Pdf

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.

Author : R.V. Ambartzumian
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939219

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Stochastic and Integral Geometry by R.V. Ambartzumian Pdf

Author : Wilfrid S. Kendall
Publisher : Routledge
Page : 424 pages
File Size : 47,7 Mb
Release : 2019-06-10
Category : Mathematics
ISBN : 9781351413718

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Stochastic Geometry by Wilfrid S. Kendall Pdf

Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

Author : Martin Haenggi
Publisher : Cambridge University Press
Page : 301 pages
File Size : 43,6 Mb
Release : 2013
Category : Computers
ISBN : 9781107014695

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Stochastic Geometry for Wireless Networks by Martin Haenggi Pdf

Analyse wireless network performance and improve design choices for future architectures and protocols with this rigorous introduction to stochastic geometry.

Author : François Baccelli,Bartłomiej Błaszczyszyn
Publisher : Now Publishers Inc
Page : 224 pages
File Size : 41,7 Mb
Release : 2009
Category : Computers
ISBN : 9781601982643

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Stochastic Geometry and Wireless Networks by François Baccelli,Bartłomiej Błaszczyszyn Pdf

This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes.

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Page : 346 pages
File Size : 43,5 Mb
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319052335

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Stochastic Analysis for Poisson Point Processes by Giovanni Peccati,Matthias Reitzner Pdf

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Author : W. Weil,A. Baddeley,I. Bárány,R. Schneider
Publisher : Springer
Page : 292 pages
File Size : 53,5 Mb
Release : 2006-10-26
Category : Mathematics
ISBN : 9783540381754

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Stochastic Geometry by W. Weil,A. Baddeley,I. Bárány,R. Schneider Pdf

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.

Author : Fabrice Baudoin
Publisher : World Scientific
Page : 152 pages
File Size : 40,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9781860944819

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An Introduction to the Geometry of Stochastic Flows by Fabrice Baudoin Pdf

This book aims to provide a self-contained introduction to the local geometry of the stochastic flows associated with stochastic differential equations. It stresses the 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 whose main tools are introduced throughout the text. By using the connection between stochastic flows and partial differential equations, we apply this point of view of the study of hypoelliptic operators written in Hormander's form.

Author : Rolf Schneider,Wolfgang Weil
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 44,6 Mb
Release : 2008-09-08
Category : Mathematics
ISBN : 9783540788591

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Stochastic and Integral Geometry by Rolf Schneider,Wolfgang Weil Pdf

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 : Volker Schmidt
Publisher : Springer
Page : 464 pages
File Size : 54,7 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319100647

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Stochastic Geometry, Spatial Statistics and Random Fields by Volker Schmidt Pdf

This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

Author : Xavier Descombes
Publisher : John Wiley & Sons
Page : 215 pages
File Size : 45,6 Mb
Release : 2013-05-06
Category : Technology & Engineering
ISBN : 9781118601136

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Stochastic Geometry for Image Analysis by Xavier Descombes Pdf

This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.

Author : Evgeny Spodarev
Publisher : Springer
Page : 446 pages
File Size : 42,6 Mb
Release : 2013-02-11
Category : Mathematics
ISBN : 9783642333057

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Stochastic Geometry, Spatial Statistics and Random Fields by Evgeny Spodarev Pdf

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 : Ya.I. Belopolskaya,Yu.L. Dalecky
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400922150

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Stochastic Equations and Differential Geometry by Ya.I. Belopolskaya,Yu.L. Dalecky Pdf

'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Anders Lindquist,Giorgio Picci
Publisher : Springer
Page : 781 pages
File Size : 40,8 Mb
Release : 2015-04-24
Category : Science
ISBN : 9783662457504

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Linear Stochastic Systems by Anders Lindquist,Giorgio Picci Pdf

This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.