Stochastic and Integral Geometry

Author: Rolf Schneider,Wolfgang Weil

Publisher: Springer Science & Business Media

ISBN: 354078859X

Category: Mathematics

Page: 694

View: 7210

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.
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Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann

Publisher: Springer-Verlag

ISBN: 364238160X

Category: Mathematics

Page: 428

View: 2445

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​
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Integral Geometry and Geometric Probability

Author: Luis A. Santaló

Publisher: Cambridge University Press

ISBN: 9780521523448

Category: Mathematics

Page: 404

View: 4367

Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.
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Factorization Calculus and Geometric Probability

Author: R. V. Ambartzumian

Publisher: Cambridge University Press

ISBN: 9780521345354

Category: Mathematics

Page: 286

View: 8933

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.
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Stochastic Geometry and Its Applications

Author: Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke

Publisher: John Wiley & Sons

ISBN: 1118658256

Category: Mathematics

Page: 584

View: 1660

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.
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Encyclopaedia of Mathematics

Stochastic Approximation — Zygmund Class of Functions

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9401512337

Category: Mathematics

Page: 536

View: 2125

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
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Integralgeometrie

Author: Rolf Schneider,Wolfgang Weil

Publisher: Springer-Verlag

ISBN: 3322848248

Category: Technology & Engineering

Page: 222

View: 2657

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Elementary Applications of Probability Theory, Second Edition

Author: Henry C. Tuckwell

Publisher: CRC Press

ISBN: 9780412576201

Category: Mathematics

Page: 296

View: 8082

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.
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Stochastic Geometry, Spatial Statistics and Random Fields

Asymptotic Methods

Author: Evgeny Spodarev

Publisher: Springer

ISBN: 3642333052

Category: Mathematics

Page: 446

View: 3501

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.
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Encyclopaedia of Mathematics

An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia"

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9934

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Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Author: Eva B. Vedel Jensen,Markus Kiderlen

Publisher: Springer

ISBN: 3319519514

Category: Mathematics

Page: 462

View: 3076

The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
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Probability Theory and Its Applications in China

Author: Shijian Yan,Chung-Chun Yang

Publisher: American Mathematical Soc.

ISBN: 0821851268

Category: Mathematics

Page: 333

View: 8774

Probability theory has always been an active field of research in China, but, until recently, almost all of this research was written in Chinese. This book contains surveys by some of China's leading probabilists, with a fairly complete coverage of theoretical probability and selective coverage of applied topics. The purpose of the book is to provide an account of the most significant results in probability obtained in China in the past few decades and to promote communication between probabilists in China and those in other countries. This collection will be of interest to graduate students and researchers in mathematics and probability theory, as well as to researchers in such areas as physics, engineering, biochemistry, and information science. Among the topics covered here are: stochastic analysis, stochastic differential equations, Dirichlet forms, Brownian motion and diffusion, potential theory, geometry of manifolds, semi-martingales, jump Markov processes, interacting particle systems, entropy production of Markov processes, renewal sequences and $p$-functions, multi-parameter stochastic processes, stationary random fields, limit theorems, strong approximations, large deviations, stochastic control systems, and probability problems in information theory.
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Theory of Random Sets

Author: Ilya Molchanov

Publisher: Springer

ISBN: 144717349X

Category: Mathematics

Page: 678

View: 1612

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.
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From Elementary Probability to Stochastic Differential Equations with MAPLE®

Author: Sasha Cyganowski,Peter Kloeden,Jerzy Ombach

Publisher: Springer Science & Business Media

ISBN: 9783540426660

Category: Mathematics

Page: 310

View: 9883

This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.
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Mathematische Statistik

Author: Bartel L. van der Waerden

Publisher: Springer-Verlag

ISBN: 3642649742

Category: Mathematics

Page: 360

View: 3686

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Stochastic Calculus and Financial Applications

Author: J. Michael Steele

Publisher: Springer Science & Business Media

ISBN: 1468493051

Category: Mathematics

Page: 302

View: 8721

Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH
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Distributed Sensor Networks, Second Edition

Sensor Networking and Applications

Author: S. Sitharama Iyengar,Richard R. Brooks

Publisher: CRC Press

ISBN: 1439862885

Category: Computers

Page: 942

View: 5948

The best-selling Distributed Sensor Networks became the definitive guide to understanding this far-reaching technology. Preserving the excellence and accessibility of its predecessor, Distributed Sensor Networks, Second Edition once again provides all the fundamentals and applications in one complete, self-contained source. Ideal as a tutorial for students or as research material for engineers, the book gives readers up-to-date, practical insight on all aspects of the field. Revised and expanded, this second edition incorporates contributions from many veterans of the DARPA ISO SENSIT program as well as new material from distinguished researchers in the field. Sensor Networking and Applications focuses on sensor deployment and networking, adaptive tasking, self-configuration, and system control. In the expanded applications section, the book draws on the insight of practitioners in the field. Readers of this book may also be interested in Distributed Sensor Networks, Second Edition: Image and Sensor Signal Processing (ISBN: 9781439862827).
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Geometric Modeling in Probability and Statistics

Author: Ovidiu Calin,Constantin Udrişte

Publisher: Springer

ISBN: 3319077791

Category: Mathematics

Page: 375

View: 670

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.
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Random Fields and Geometry

Author: R. J. Adler,Jonathan E. Taylor

Publisher: Springer Science & Business Media

ISBN: 9780387481166

Category: Mathematics

Page: 454

View: 6045

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
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