Geometric Problems in the Theory of Infinite-dimensional Probability Distributions

Geometric Problems in the Theory of Infinite-dimensional Probability Distributions PDF Author: V. N. Sudakov
Publisher: American Mathematical Soc.
ISBN: 9780821830413
Category : Mathematics
Languages : en
Pages : 188

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Book Description
Discusses problems in the distribution theory of probability.

Geometric Problems in the Theory of Infinite-dimensional Probability Distributions

Geometric Problems in the Theory of Infinite-dimensional Probability Distributions PDF Author: V. N. Sudakov
Publisher: American Mathematical Soc.
ISBN: 9780821830413
Category : Mathematics
Languages : en
Pages : 188

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Book Description
Discusses problems in the distribution theory of probability.

Probability Distributions on Banach Spaces

Probability Distributions on Banach Spaces PDF Author: N Vakhania
Publisher: Springer Science & Business Media
ISBN: 940093873X
Category : Mathematics
Languages : en
Pages : 507

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Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Probability in Banach Spaces

Probability in Banach Spaces PDF Author: Michel Ledoux
Publisher: Springer Science & Business Media
ISBN: 3642202128
Category : Mathematics
Languages : en
Pages : 493

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Book Description
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

Linear and Complex Analysis Problem Book 3

Linear and Complex Analysis Problem Book 3 PDF Author: Victor P. Havin
Publisher: Springer
ISBN: 3540483675
Category : Mathematics
Languages : en
Pages : 517

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Book Description
The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!

Weak Convergence and Empirical Processes

Weak Convergence and Empirical Processes PDF Author: AW van der Vaart
Publisher: Springer Science & Business Media
ISBN: 0387946403
Category : Mathematics
Languages : en
Pages : 531

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Book Description
This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

Introduction to Banach Spaces: Analysis and Probability: Volume 1

Introduction to Banach Spaces: Analysis and Probability: Volume 1 PDF Author: Daniel Li
Publisher: Cambridge University Press
ISBN: 110829815X
Category : Mathematics
Languages : en
Pages : 463

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Book Description
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Introduction to Banach Spaces: Analysis and Probability

Introduction to Banach Spaces: Analysis and Probability PDF Author: Daniel Li
Publisher: Cambridge University Press
ISBN: 1107160510
Category : Mathematics
Languages : en
Pages : 463

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Book Description
This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

Lectures on Probability Theory and Statistics

Lectures on Probability Theory and Statistics PDF Author: Roland Dobrushin
Publisher: Springer
ISBN: 3540496351
Category : Mathematics
Languages : en
Pages : 308

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Book Description


Introduction to Banach Spaces: Analysis and Probability: Volume 2

Introduction to Banach Spaces: Analysis and Probability: Volume 2 PDF Author: Daniel Li
Publisher: Cambridge University Press
ISBN: 1108298168
Category : Mathematics
Languages : en
Pages : 405

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Book Description
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

High-Dimensional Probability

High-Dimensional Probability PDF Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299

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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.