Stochastic Geometric Analysis With Applications

Author : Ovidiu Calin
Publisher : World Scientific
Page : 557 pages
File Size : 44,5 Mb
Release : 2023-11-21
Category : Mathematics
ISBN : 9789811283291

Get Book

Stochastic Geometric Analysis With Applications by Ovidiu Calin Pdf

This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.

Author : David Coupier
Publisher : Springer
Page : 232 pages
File Size : 43,9 Mb
Release : 2019-04-09
Category : Mathematics
ISBN : 9783030135478

Get Book

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 : Dietrich Stoyan,Wilfrid S. Kendall
Publisher : Wiley
Page : 458 pages
File Size : 54,7 Mb
Release : 2009-03-16
Category : Mathematics
ISBN : 0470743646

Get Book

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 : Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke
Publisher : John Wiley & Sons
Page : 561 pages
File Size : 54,9 Mb
Release : 2013-06-27
Category : Mathematics
ISBN : 9781118658253

Get Book

Stochastic Geometry and Its Applications by Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke Pdf

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, 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 previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Page : 346 pages
File Size : 41,6 Mb
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319052335

Get Book

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 : Wilfrid S. Kendall
Publisher : Routledge
Page : 419 pages
File Size : 49,6 Mb
Release : 2019-06-10
Category : Mathematics
ISBN : 9781351413725

Get Book

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 : D. Kannan,V. Lakshmikantham
Publisher : CRC Press
Page : 808 pages
File Size : 50,9 Mb
Release : 2001-10-23
Category : Mathematics
ISBN : 9781482294705

Get Book

Handbook of Stochastic Analysis and Applications by D. Kannan,V. Lakshmikantham Pdf

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

Author : Rolf Schneider,Wolfgang Weil
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 46,8 Mb
Release : 2008-09-08
Category : Mathematics
ISBN : 9783540788591

Get Book

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 : Viktor Benes,Jan Rataj
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 43,6 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9781402081033

Get Book

Stochastic Geometry by Viktor Benes,Jan Rataj Pdf

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.

Author : Dan Crisan
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 40,6 Mb
Release : 2010-11-26
Category : Mathematics
ISBN : 9783642153587

Get Book

Stochastic Analysis 2010 by Dan Crisan Pdf

Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume “Stochastic Analysis 2010” provides a sample of the current research in the different branches of the subject. It includes the collected works of the participants at the Stochastic Analysis section of the 7th ISAAC Congress organized at Imperial College London in July 2009.

Author : Xavier Descombes
Publisher : John Wiley & Sons
Page : 215 pages
File Size : 53,9 Mb
Release : 2013-05-06
Category : Technology & Engineering
ISBN : 9781118601136

Get Book

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 : R.V. Ambartzumian
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939219

Get Book

Stochastic and Integral Geometry by R.V. Ambartzumian Pdf

Author : Wilfrid S. Kendall,Ilya Molchanov
Publisher : OUP Oxford
Page : 606 pages
File Size : 47,8 Mb
Release : 2009-11-26
Category : Mathematics
ISBN : 0199232571

Get Book

New Perspectives in Stochastic Geometry by Wilfrid S. Kendall,Ilya Molchanov Pdf

A collection of chapters from leading scholars on the subject of stochastic geometry, laying the foundations for future research and providing fresh perspectives, ideas and interdisciplinary connections now arising from Stochastic Geometry.

Author : Bartłomiej Błaszczyszyn,Martin Haenggi,Paul Keeler,Sayandev Mukherjee
Publisher : Cambridge University Press
Page : 207 pages
File Size : 52,8 Mb
Release : 2018-04-19
Category : Mathematics
ISBN : 9781107162587

Get Book

Stochastic Geometry Analysis of Cellular Networks by Bartłomiej Błaszczyszyn,Martin Haenggi,Paul Keeler,Sayandev Mukherjee Pdf

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Author : Ilya S. Molchanov,W. S. Kendall
Publisher : Unknown
Page : 585 pages
File Size : 44,5 Mb
Release : 2010
Category : Stochastic geometry
ISBN : 0191716391

Get Book

New Perspectives in Stochastic Geometry by Ilya S. Molchanov,W. S. Kendall Pdf

A collection of chapters from leading scholars on the subject of stochastic geometry, laying the foundations for future research and providing fresh perspectives, ideas and interdisciplinary connections now arising from stochastic geometry.