Author: Jean-Benoît Bost
Publisher: Birkhäuser
ISBN: 3319496387
Category : Mathematics
Languages : fr
Pages : 363
Book Description
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Geometry, Analysis and Probability
Author: Jean-Benoît Bost
Publisher: Birkhäuser
ISBN: 3319496387
Category : Mathematics
Languages : fr
Pages : 363
Book Description
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Publisher: Birkhäuser
ISBN: 3319496387
Category : Mathematics
Languages : fr
Pages : 363
Book Description
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Geometry, Analysis and Probability
Author: Jean-Benoît Bost
Publisher:
ISBN: 9783319496375
Category : Distribution (Probability theory)
Languages : en
Pages : 361
Book Description
Publisher:
ISBN: 9783319496375
Category : Distribution (Probability theory)
Languages : en
Pages : 361
Book Description
Introduction to Geometric Probability
Author: Daniel A. Klain
Publisher: Cambridge University Press
ISBN: 9780521596541
Category : Mathematics
Languages : en
Pages : 196
Book Description
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.
Publisher: Cambridge University Press
ISBN: 9780521596541
Category : Mathematics
Languages : en
Pages : 196
Book Description
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.
Geometric Modeling in Probability and Statistics
Author: Ovidiu Calin
Publisher: Springer
ISBN: 3319077791
Category : Mathematics
Languages : en
Pages : 389
Book Description
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.
Publisher: Springer
ISBN: 3319077791
Category : Mathematics
Languages : en
Pages : 389
Book Description
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.
Differential Geometry and Statistics
Author: M.K. Murray
Publisher: Routledge
ISBN: 1351455117
Category : Mathematics
Languages : en
Pages : 292
Book Description
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Publisher: Routledge
ISBN: 1351455117
Category : Mathematics
Languages : en
Pages : 292
Book Description
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Analysis, Geometry, and Probability
Author: R. Chuaqui
Publisher:
ISBN: 9780824474195
Category : Geometry
Languages : en
Pages : 0
Book Description
Publisher:
ISBN: 9780824474195
Category : Geometry
Languages : en
Pages : 0
Book Description
Analysis and Geometry on Groups
Author: Nicholas T. Varopoulos
Publisher: Cambridge University Press
ISBN: 9780521353823
Category : Mathematics
Languages : en
Pages : 172
Book Description
The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.
Publisher: Cambridge University Press
ISBN: 9780521353823
Category : Mathematics
Languages : en
Pages : 172
Book Description
The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.
Fractals in Probability and Analysis
Author: Christopher J. Bishop
Publisher: Cambridge University Press
ISBN: 1107134110
Category : Mathematics
Languages : en
Pages : 415
Book Description
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Publisher: Cambridge University Press
ISBN: 1107134110
Category : Mathematics
Languages : en
Pages : 415
Book Description
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Analysis, Geometry and Probability
Author: Rajendra Bhatia
Publisher: Springer
ISBN: 9380250878
Category : Mathematics
Languages : en
Pages : 425
Book Description
This book is a collection of expository articles by well-known mathematicians. Some of them introduce the reader to a major topic, while others provide a glimpse into an active field of research. All articles are accessible to graduate students. The articles were invited in honour of K. R. Parthasarathy, a mathematican, teacher and expositor of renown. Some of the articles, by his coworkers, are related to his work on probability, quantum probability and group representations. Others are on diverse topics in analysis, geometry and number theory.
Publisher: Springer
ISBN: 9380250878
Category : Mathematics
Languages : en
Pages : 425
Book Description
This book is a collection of expository articles by well-known mathematicians. Some of them introduce the reader to a major topic, while others provide a glimpse into an active field of research. All articles are accessible to graduate students. The articles were invited in honour of K. R. Parthasarathy, a mathematican, teacher and expositor of renown. Some of the articles, by his coworkers, are related to his work on probability, quantum probability and group representations. Others are on diverse topics in analysis, geometry and number theory.
Analysis, Geometry, and Modeling in Finance
Author: Pierre Henry-Labordere
Publisher: CRC Press
ISBN: 1420087002
Category : Business & Economics
Languages : en
Pages : 403
Book Description
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th
Publisher: CRC Press
ISBN: 1420087002
Category : Business & Economics
Languages : en
Pages : 403
Book Description
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th