**Author**: N Vakhania

**Publisher:**

**ISBN:**

**Category:** Espacios de Banach

**Page:** 512

**View:** 925

- 1987-10-31
- in Espacios de Banach
- N Vakhania

**Author**: N Vakhania

**Publisher:**

**ISBN:**

**Category:** Espacios de Banach

**Page:** 512

**View:** 925

- 1987-10-31
- in Mathematics
- N Vakhania

**Author**: N Vakhania

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 482

**View:** 857

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.

- 2012-12-06
- in Mathematics
- N Vakhania

**Author**: N Vakhania

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 482

**View:** 389

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.

- 2006-11-14
- in Mathematics
- Anatole Beck

*Proceedings of the International Conference held in Medford, USA, July 16-27, 1984*

**Author**: Anatole Beck

**Publisher:** Springer

**ISBN:**

**Category:** Mathematics

**Page:** 460

**View:** 621

- 1979
- in Mathematics
- V. N. Sudakov

**Author**: V. N. Sudakov

**Publisher:** American Mathematical Soc.

**ISBN:**

**Category:** Mathematics

**Page:** 178

**View:** 312

Discusses problems in the distribution theory of probability.

- 1981
- in Distribution (Probability theory).
- Nikolaĭ Nikolaevich Vakhanii͡a

**Author**: Nikolaĭ Nikolaevich Vakhanii͡a

**Publisher:** North-Holland

**ISBN:**

**Category:** Distribution (Probability theory).

**Page:** 123

**View:** 443

- 1991
- in Language Arts & Disciplines
- Michel Ledoux

*Isoperimetry and Processes*

**Author**: Michel Ledoux

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Language Arts & Disciplines

**Page:** 480

**View:** 466

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.

- 2013-03-09
- in Mathematics
- Michel Ledoux

*Isoperimetry and Processes*

**Author**: Michel Ledoux

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 480

**View:** 426

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.

- 2012-12-06
- in Mathematics
- R.M. Dudley

**Author**: R.M. Dudley

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 512

**View:** 808

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.

- 1996-01-01
- in Mathematics
- IU. IUrii Vasilevich Borovskikh

**Author**: IU. IUrii Vasilevich Borovskikh

**Publisher:** VSP

**ISBN:**

**Category:** Mathematics

**Page:** 420

**View:** 729

U-statistics are universal objects of modern probabilistic summation theory. They appear in various statistical problems and have very important applications. The mathematical nature of this class of random variables has a functional character and, therefore, leads to the investigation of probabilistic distributions in infinite-dimensional spaces. The situation when the kernel of a U-statistic takes values in a Banach space, turns out to be the most natural and interesting. In this book, the author presents in a systematic form the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), which has been developed to date. The exposition of the material in this book is based around the following topics: algebraic and martingale properties of U-statistics; inequalities; law of large numbers; the central limit theorem; weak convergence to a Gaussian chaos and multiple stochastic integrals; invariance principle and functional limit theorems; estimates of the rate of weak convergence; asymptotic expansion of distributions; large deviations; law of iterated logarithm; dependent variables; relation between Banach-valued U-statistics and functionals from permanent random measures.

- 1983
- in Mathematics
- Werner Linde

**Author**: Werner Linde

**Publisher:** John Wiley & Sons Incorporated

**ISBN:**

**Category:** Mathematics

**Page:** 195

**View:** 404

This book is devoted to the study of stable measures on Banach spaces. The first part presents the classical approach via infinitely divisible measures (the Levy-Khinchin representation) and establishes some general properties of stable measures, such as Levy's spectral representation and the tail behaviour of stable measures. The second part is devoted to a comparatively new functional analytic approach, and an investigation is made of operators T from E' to Lp which generate p-stable symmetric measures on the Banach space E.

- 2006-11-14
- in Mathematics
- A. Beck

*Proceedings of the Second International Conference on Probability in Banach Spaces, 18-24 June 1978, Oberwolfach, Germany*

**Author**: A. Beck

**Publisher:** Springer

**ISBN:**

**Category:** Mathematics

**Page:** 212

**View:** 136

- 2007-12-31
- in Mathematics
- Albrecht Pietsch

**Author**: Albrecht Pietsch

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 855

**View:** 398

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

- 2020-01-01
- in Mathematics
- Nathael Gozlan

*The Oaxaca Volume*

**Author**: Nathael Gozlan

**Publisher:** Springer Nature

**ISBN:**

**Category:** Mathematics

**Page:** 458

**View:** 152

This volume collects selected papers from the 8th High Dimensional Probability meeting held at Casa Matemática Oaxaca (CMO), Mexico. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, random graphs, information theory and convex geometry. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.

- 2016-09-21
- in Mathematics
- Christian Houdré

*The Cargèse Volume*

**Author**: Christian Houdré

**Publisher:** Birkhäuser

**ISBN:**

**Category:** Mathematics

**Page:** 461

**View:** 980

This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'Études Scientifiques de Cargèse (IESC) in Corsica, France. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, and random graphs. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.

- 1976-07
- in Mathematics
- Anatole Beck

*Proceedings of the First International Conference on Probability in Banach Spaces, 20 - 26 July 1975, Oberwolfach*

**Author**: Anatole Beck

**Publisher:** Springer Verlag

**ISBN:**

**Category:** Mathematics

**Page:** 290

**View:** 644

- 2013-01-04
- in Mathematics
- Svetlozar T. Rachev

**Author**: Svetlozar T. Rachev

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 619

**View:** 548

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute—Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)

- 2003-10-03
- in Mathematics
- Fred W. Steutel

**Author**: Fred W. Steutel

**Publisher:** CRC Press

**ISBN:**

**Category:** Mathematics

**Page:** 550

**View:** 805

Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.

- 2018-02-14
- in Mathematics
- Tuomas Hytönen

*Volume II: Probabilistic Methods and Operator Theory*

**Author**: Tuomas Hytönen

**Publisher:** Springer

**ISBN:**

**Category:** Mathematics

**Page:** 616

**View:** 992

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.

- 1996-08
- in Mathematics
- P. Wojtaszczyk

**Author**: P. Wojtaszczyk

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Mathematics

**Page:** 382

**View:** 821

This book is intended to be used with graduate courses in Banach space theory.