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Stochastic Geometric Analysis With Applications

2023-11-21 Mathematics
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Release : 2023-11-21
Genre : Mathematics
Kind : eBook
Book Rating : 29X/5 ( reviews)

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Book Synopsis Stochastic Geometric Analysis With Applications by : Ovidiu Calin

Download or read book Stochastic Geometric Analysis With Applications written by Ovidiu Calin. This book was released on 2023-11-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Geometry

2019-06-10 Mathematics
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Release : 2019-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 724/5 ( reviews)

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Book Synopsis Stochastic Geometry by : Wilfrid S. Kendall

Download or read book Stochastic Geometry written by Wilfrid S. Kendall. This book was released on 2019-06-10. Available in PDF, EPUB and Kindle. Book excerpt: 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

Stochastic and Integral Geometry

2008-09-08 Mathematics
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Release : 2008-09-08
Genre : Mathematics
Kind : eBook
Book Rating : 59X/5 ( reviews)

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Book Synopsis Stochastic and Integral Geometry by : Rolf Schneider

Download or read book Stochastic and Integral Geometry written by Rolf Schneider. This book was released on 2008-09-08. 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.

Stochastic Geometry and its Applications

2009-03-16 Mathematics
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Release : 2009-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 645/5 ( reviews)

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Book Synopsis Stochastic Geometry and its Applications by : Dietrich Stoyan

Download or read book Stochastic Geometry and its Applications written by Dietrich Stoyan. This book was released on 2009-03-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Geometry

2019-04-09 Mathematics
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Release : 2019-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 470/5 ( reviews)

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Book Synopsis Stochastic Geometry by : David Coupier

Download or read book Stochastic Geometry written by David Coupier. This book was released on 2019-04-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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