Probability In Banach Spaces

Author : Michel Ledoux,Michel Talagrand
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783642202124

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Probability in Banach Spaces by Michel Ledoux,Michel Talagrand Pdf

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.

Author : Michel Ledoux,Michel Talagrand
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 45,5 Mb
Release : 1991
Category : Language Arts & Disciplines
ISBN : 3540520139

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Probability in Banach Spaces by Michel Ledoux,Michel Talagrand Pdf

Based on recent developments, such as new isoperimetric inequalities and random process techniques, this book presents a thorough treatment of the main aspects of Probability in Banach spaces, and of some of their links to Geometry of Banach spaces.

Author : Jorgen Hoffmann-Jorgensen,James Kuelbs,Michael B. Marcus
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202530

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Probability in Banach Spaces, 9 by Jorgen Hoffmann-Jorgensen,James Kuelbs,Michael B. Marcus Pdf

The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, even about familiar processes, by stripping away details, that in hindsight turn out to be extraneous. A good understanding about the disciplines involved in this field can be obtained from the recent book, Probability in Banach Spaces, Springer-Verlag, by M. Ledoux and M. Thlagrand. On page 5, of this book, there is a list of previous conferences in probability in Banach spaces, including the other eight international conferences. One can see that research in this field over the last twenty years has contributed significantly to knowledge in probability and has had important applications in many other branches of mathematics, most notably in statistics and functional analysis.

Author : N Vakhania,Vazha Tarieladze,S. Chobanyan
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400938731

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Probability Distributions on Banach Spaces by N Vakhania,Vazha Tarieladze,S. Chobanyan Pdf

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.

Author : R.M. Dudley,M.G. Hahn,J. Kuelbs
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203674

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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference by R.M. Dudley,M.G. Hahn,J. Kuelbs Pdf

Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.

Author : Anatole Beck
Publisher : Springer
Page : 291 pages
File Size : 55,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382560

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Probability in Banach Spaces by Anatole Beck Pdf

Author : Eberlein,Külbs,Marcus
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468405590

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Probability in Banach Spaces 7 by Eberlein,Külbs,Marcus Pdf

The first international conference on Probability in Banach Spaces was held at Oberwolfach, West Germany, in 1975. It brought together European researchers who, under the inspiration of the Schwartz Seminar in Paris, were using probabi listic methods in the study of the geometry of Banach spaces, a rather small number of probabilists who were already studying classical limit laws on Banach spaces, and a larger number of probabilists, specialists in various aspects of the study of Gaussian processes, whose results and techniques were of interest to the members of the first two groups. This first conference was very fruitful. It fos tered a continuing relationship among 50 to 75 probabilists and analysts working on probability on infinite-dimensional spaces, the geometry of Banach spaces, and the use of random methods in harmonic analysis. Six more international conferences were held since the 1975 meeting. Two of the meetings were held at Tufts University, one at S¢nderborg, Denmark, and the others at Oberwolfach. This volume contains a selection of papers by the partici pants of the Seventh International Conference held at Oberwolfach, West Ger many, June 26-July 2, 1988. This exciting and provocative conference was at tended by more than 50 mathematicians from many countries. These papers demonstrate the range of interests of the conference participants. In addition to the ongoing study of classical and modern limit theorems in Banach spaces, a branching out has occurred among the members of this group.

Author : Anatole Beck,Richard Dudley,Marjorie Hahn,James Kuelbs,Michael Marcus
Publisher : Springer
Page : 463 pages
File Size : 46,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540396451

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Probability in Banach Spaces V by Anatole Beck,Richard Dudley,Marjorie Hahn,James Kuelbs,Michael Marcus Pdf

Author : Michel LeDoux,Michel Talagrand
Publisher : Springer
Page : 500 pages
File Size : 42,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3642202136

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Probability in Banach Spaces by Michel LeDoux,Michel Talagrand Pdf

Based on recent developments, such as new isoperimetric inequalities and random process techniques, this book presents a thorough treatment of the main aspects of Probability in Banach spaces, and of some of their links to Geometry of Banach spaces.

Author : Gilles Pisier
Publisher : Cambridge University Press
Page : 591 pages
File Size : 44,8 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781107137240

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Martingales in Banach Spaces by Gilles Pisier Pdf

This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 616 pages
File Size : 51,5 Mb
Release : 2018-02-14
Category : Mathematics
ISBN : 9783319698083

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Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 51,6 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9781441975157

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Banach Space Theory by Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler Pdf

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

Author : Anatole Beck
Publisher : Unknown
Page : 128 pages
File Size : 51,6 Mb
Release : 1976
Category : Banach spaces
ISBN : OCLC:164999577

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Probability in Banach Spaces by Anatole Beck Pdf

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 40,9 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : Anatole Beck
Publisher : Unknown
Page : 306 pages
File Size : 47,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662179083

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Probability in Banach Spaces by Anatole Beck Pdf