Geometry Of Random Motion

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Geometry of Random Motion

Author : Richard Durrett
Publisher : American Mathematical Soc.
ISBN 13 : 0821850814
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry of Random Motion by : Richard Durrett

Download or read book Geometry of Random Motion written by Richard Durrett and published by American Mathematical Soc.. This book was released on 1988 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes. Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on various geometric structures, such as Riemannian manifolds, Lie groups, and symmetric spaces. Some of the articles specifically address analysis on manifolds, while others center on (nongeometric) stochastic analysis. The majority of the articles deal simultaneously with probabilistic and geometric techniques. Requiring a knowledge of the modern theory of diffusion processes, this book will appeal to mathematicians, mathematical physicists, and other researchers interested in Brownian motion, diffusion processes, Laplace-Beltrami operators, and the geometric applications of these concepts. The book provides a detailed view of the leading edge of research in this rapidly moving field.

The Geometry of Random Fields

Author : Robert J. Adler
Publisher : SIAM
ISBN 13 : 0898716934
Total Pages : 295 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis The Geometry of Random Fields by : Robert J. Adler

Download or read book The Geometry of Random Fields written by Robert J. Adler and published by SIAM. This book was released on 2010-01-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Galileo Unbound

Author : David D. Nolte
Publisher : Oxford University Press
ISBN 13 : 0192528505
Total Pages : 384 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Galileo Unbound by : David D. Nolte

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Stochastic and Integral Geometry

Author : Rolf Schneider
Publisher : Springer Science & Business Media
ISBN 13 : 354078859X
Total Pages : 692 pages
Book Rating : 4.5/5 (47 download)

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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 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.

Topics in Modern Differential Geometry

Author : Stefan Haesen
Publisher : Springer
ISBN 13 : 9462392404
Total Pages : 289 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Topics in Modern Differential Geometry by : Stefan Haesen

Download or read book Topics in Modern Differential Geometry written by Stefan Haesen and published by Springer. This book was released on 2016-12-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

Analysis and Geometry on Graphs and Manifolds

Author : Matthias Keller
Publisher : Cambridge University Press
ISBN 13 : 1108587380
Total Pages : 493 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Analysis and Geometry on Graphs and Manifolds by : Matthias Keller

Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

Introduction to Geometric Probability

Author : Daniel A. Klain
Publisher : Cambridge University Press
ISBN 13 : 9780521596541
Total Pages : 196 pages
Book Rating : 4.5/5 (965 download)

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Book Synopsis Introduction to Geometric Probability by : Daniel A. Klain

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: The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.

Mysterious Motions and Other Intriguing Phenomena in Physics

Author : G. Ranganath
Publisher : Universities Press
ISBN 13 : 9788173714016
Total Pages : 166 pages
Book Rating : 4.7/5 (14 download)

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Book Synopsis Mysterious Motions and Other Intriguing Phenomena in Physics by : G. Ranganath

Download or read book Mysterious Motions and Other Intriguing Phenomena in Physics written by G. Ranganath and published by Universities Press. This book was released on 2002 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book dwells upon intriguing examples and situations that are not generally analysed or discussed in standard textbook and formal couses in physics. In this book, a majority of the examples are from classical physics, which forms an essential part of our education. Each of the six chapters covers a major area of physics, and is subdivided into sections, each of which has a runing theme.

Rational Bubbles

Author : Matthias Salge
Publisher : Springer Science & Business Media
ISBN 13 : 3642591817
Total Pages : 270 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Rational Bubbles by : Matthias Salge

Download or read book Rational Bubbles written by Matthias Salge and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3 On the Economic Relevance of Rational Bubbles 79 3. 1 Capital markets . . . . . . . . . 80 3. 1. 1 Efficient capital markets 86 3. 1. 2 Rational bubbles on capital markets. 93 3. 1. 3 Economic caveats . 103 3. 2 Foreign exchange markets 109 3. 3 Hyperinflation. . . . . . . 117 4 On Testing for Rational Bubbles 123 4. 1 Indirect tests . . . . . . . . . 123 4. 1. 1 Variance bounds tests 124 4. 1. 2 Specification tests . . . 137 4. 1. 3 Integration and cointegration tests 140 4. 1. 4 Final assessment of indirect tests . 150 4. 1. 5 A digression: Charemza, Deadman (1995) analysis. 151 4. 2 Direct tests . . . . . . . . . . . . . . . . . . . . . . . . 157 4. 2. 1 Deterministic bubble in German hyperinflation. 158 4. 2. 2 Intrinsic bubbles on stock markets. 163 4. 2. 3 An econometric caveat . . . . . 168 4. 2. 4 Final assessment of direct tests 172 5 On the Explanatory Power of Rational Bubbles on the G- man Stock Market 175 5. 1 Data . . . . . . . 175 5. 2 Direct test for rational bubbles 181 5. 2. 1 Temporary Markovian bubbles. 184 5. 2. 2 Temporary intrinsic bubbles . . 193 ix 5. 2. 3 Permanent intrinsic bubbles 198 5. 3 A digression: Testing for unit roots 204 6 Concluding Remarks 215 A Results 221 A. 1 Temporary markovian bubbles. 221 A. 2 Temporary intrinsic bubbles . . 225 A. 3 Permanent intrinsic bubbles - Class 1 to 2 229 A. 4 Permanent intrinsic bubbles - Class 3 to 6 230 A. 5 Integration tests. . . . . . . . . . . . . . .

Geometric and Probabilistic Structures in Dynamics

Author : Keith Burns
Publisher : American Mathematical Soc.
ISBN 13 : 0821842862
Total Pages : 358 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric and Probabilistic Structures in Dynamics by : Keith Burns

Download or read book Geometric and Probabilistic Structures in Dynamics written by Keith Burns and published by American Mathematical Soc.. This book was released on 2008 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

Cognitive Development and Cognitive Neuroscience

Author : Usha Goswami
Publisher : Routledge
ISBN 13 : 1317410041
Total Pages : 925 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Cognitive Development and Cognitive Neuroscience by : Usha Goswami

Download or read book Cognitive Development and Cognitive Neuroscience written by Usha Goswami and published by Routledge. This book was released on 2019-09-26 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cognitive Development and Cognitive Neuroscience: The Learning Brain is a thoroughly revised edition of the bestselling Cognitive Development. The new edition of this full-colour textbook has been updated with the latest research in cognitive neuroscience, going beyond Piaget and traditional theories to demonstrate how emerging data from the brain sciences require a new theoretical framework for teaching cognitive development, based on learning. Building on the framework for teaching cognitive development presented in the first edition, Goswami shows how different cognitive domains such as language, causal reasoning and theory of mind may emerge from automatic neural perceptual processes. Cognitive Neuroscience and Cognitive Development integrates principles and data from cognitive science, neuroscience, computer modelling and studies of non-human animals into a model that transforms the study of cognitive development to produce both a key introductory text and a book which encourages the reader to move beyond the superficial and gain a deeper understanding of the subject matter. Cognitive Development and Cognitive Neuroscience is essential for students of developmental and cognitive psychology, education, language and the learning sciences. It will also be of interest to anyone training to work with children.

Geometric Aspects of Probability Theory and Mathematical Statistics

Author : V.V. Buldygin
Publisher : Springer Science & Business Media
ISBN 13 : 9401716870
Total Pages : 314 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Geometric Aspects of Probability Theory and Mathematical Statistics by : V.V. Buldygin

Download or read book Geometric Aspects of Probability Theory and Mathematical Statistics written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.

Statistics and Finance

Author : David Ruppert
Publisher : Springer
ISBN 13 : 1441968768
Total Pages : 488 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Statistics and Finance by : David Ruppert

Download or read book Statistics and Finance written by David Ruppert and published by Springer. This book was released on 2014-02-26 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the applications of statistics and probability to finance. The basics of these subjects are reviewed and more advanced topics in statistics, such as regression, ARMA and GARCH models, the bootstrap, and nonparametric regression using splines, are introduced as needed. The book covers the classical methods of finance and it introduces the newer area of behavioral finance. Applications and use of MATLAB and SAS software are stressed. The book will serve as a text in courses aimed at advanced undergraduates and masters students. Those in the finance industry can use it for self-study.

Random Fields and Geometry

Author : R. J. Adler
Publisher : Springer Science & Business Media
ISBN 13 : 0387481168
Total Pages : 455 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Random Fields and Geometry by : R. J. Adler

Download or read book Random Fields and Geometry written by R. J. Adler and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Geometric Methods in Mathematical Physics

Author : Jerrold E. Marsden
Publisher : SIAM
ISBN 13 : 0898711703
Total Pages : 103 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Geometric Methods in Mathematical Physics by : Jerrold E. Marsden

Download or read book Lectures on Geometric Methods in Mathematical Physics written by Jerrold E. Marsden and published by SIAM. This book was released on 1981-01-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Recent Developments in Geometry

Author : Robert Everist Greene
Publisher : American Mathematical Soc.
ISBN 13 : 0821851071
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Geometry by : Robert Everist Greene

Download or read book Recent Developments in Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1989 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outgrowth of a Special Session on Geometry, held at the November 1987 meeting of the AMS at the University of California at Los Angeles. The unusually well-attended session attracted more than sixty participants and featured over forty addresses by some of the day's outstanding geometers. By common consent, it was decided that the papers to be collected in the present volume should be surveys of relatively broad areas of geometry, rather than detailed presentations of new research results. A comprehensive survey of the field is beyond the scope of a volume such as this. Nonetheless, the editors have sought to provide all geometers, whatever their specialties, with some insight into recent developments in a variety of topics in this active area of research.

A Practical Guide to Geometric Regulation for Distributed Parameter Systems

Author : Eugenio Aulisa
Publisher : CRC Press
ISBN 13 : 1420061356
Total Pages : 1266 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis A Practical Guide to Geometric Regulation for Distributed Parameter Systems by : Eugenio Aulisa

Download or read book A Practical Guide to Geometric Regulation for Distributed Parameter Systems written by Eugenio Aulisa and published by CRC Press. This book was released on 2015-06-18 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems. The first part of the book is devoted to regulation of linear systems, beginning with the mathematical setup, general theory, and solution strategy for regulation problems with bounded input and output operators. The book then considers the more interesting case of unbounded control and sensing. Mathematically, this case is more complicated and general theorems in this area have become available only recently. The authors also provide a collection of interesting linear regulation examples from physics and engineering. The second part focuses on regulation for nonlinear systems. It begins with a discussion of theoretical results, characterizing solvability of nonlinear regulator problems with bounded input and output operators. The book progresses to problems for which the geometric theory based on center manifolds does not directly apply. The authors show how the idea of attractive invariance can be used to solve a series of increasingly complex regulation problems. The book concludes with the solutions of challenging nonlinear regulation examples from physics and engineering.