Probability Distributions on Banach Spaces

Author: N Vakhania,Vazha Tarieladze,S. Chobanyan

Publisher: Springer Science & Business Media

ISBN: 940093873X

Category: Mathematics

Page: 482

View: 5588

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.
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Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference

proceeding of the Eighth International Conference [celebrado en verano de 1991 en Bowdoin College]

Author: R.M. Dudley,M.G. Hahn,James Kuelbs

Publisher: Springer Science & Business Media

ISBN: 9780817636579

Category: Mathematics

Page: 510

View: 7417

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.
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Probability in Banach Spaces

Isoperimetry and Processes

Author: Michel Ledoux,Michel Talagrand

Publisher: Springer Science & Business Media

ISBN: 3642202128

Category: Mathematics

Page: 480

View: 932

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.
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Introduction to Banach Spaces: Analysis and Probability:

Author: Daniel Li,Hervé Queffélec

Publisher: Cambridge University Press

ISBN: 1108300081

Category: Mathematics

Page: N.A

View: 553

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.
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Asymptotic Methods in Probability and Statistics with Applications

Author: N. Balakrishnan,I.A.V.B. Ibragimov,Valery B. Nevzorov

Publisher: Springer Science & Business Media

ISBN: 9780817642143

Category: Business & Economics

Page: 549

View: 3854

This book represents thirty-eight extensive and carefully edited chapters written by prominent researchers, providing an up-to-date survey of new asymptotic methods in science and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of asymptotic methods in probability and mathematical statistics. The book is organized into ten thematic parts: probability distributions; characterizations of distributions; probabilities and measures in high dimensional structures; weak and stron limit theorems; large deviation probabilities; empirical processes; order statistics and records; estimation of parameters and hypotheses testing; random walks, and applications to finance. Written in an accessible style, this book conveys a clear and practical perspective of asymptotic methods. Topics and features:Recent developments in asymptotic methods; Parametric and Nonparametric Inference; Distribution Theory; Stochastic Processes; Order Statistics; Record values and Characterizations. Asymptotic methods in Probability and Mathematical Statistics is an essential resource for reseachers, practitioners, and professionals involved in Theoretical and Applied Probability and/or in Theoretical and Applied Statistics. Various chapters of the volume will also appeal to industrial statisticians and financial economists.
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Probability in Banach spaces 6

proceedings of the sixth international conference Sandbjerg, Denmark, 1986

Author: U. Haagerup,Jørgen Hoffmann-Jørgensen,N. J. Nielsen

Publisher: Birkhauser

ISBN: 9780817634940

Category: Mathematics

Page: 288

View: 7406

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Functional Analysis and its Applications

Proceedings of the International Conference on Functional Analysis and its Applications dedicated to the 110th Anniversary of Stefan Banach, May 28-31, 2002, Lviv, Ukraine

Author: Vladimir Kadets,Wieslaw Tadeusz Zelazko

Publisher: Elsevier

ISBN: 9780080472805

Category: Mathematics

Page: 342

View: 9999

The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach ƒ{ the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.
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Gaussian Hilbert Spaces

Author: Svante Janson

Publisher: Cambridge University Press

ISBN: 9780521561280

Category: Mathematics

Page: 340

View: 1622

This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.
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Probability in Banach Spaces

Proceedings of the ... International Conference on Probability in Banach Spaces

Author: U. Haagerup,Jørgen Hoffmann-Jørgensen,N. J. Nielsen

Publisher: Birkhauser

ISBN: 9780817634940

Category: Probabilities

Page: 288

View: 7907

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Strict Convexity and Complex Strict Convexity

Theory and Applications

Author: Istratescu

Publisher: CRC Press

ISBN: 9780824717964

Category: Mathematics

Page: 336

View: 6744

This important work provides a comprehensive overview of the properties of Banachspaces related to strict convexity and a survey of significant applications-uniting a wealthof information previously scattered throughout the mathematical literature in a well-organized, accessible format.After introducing the subject through a discussion of the basic results of linear functionalanalysis, this unique book proceeds to investigate the characteristics of strictly convexspaces and related classes, including uniformly convex spaces, and examine important applicationsregarding approximation theory and fixed point theory. Following this extensivetreatment, the book discusses complex strictly convex spaces and related spaces- alsowith applications. Complete, clearly elucidated proofs accompany results throughout thebook, and ample references are provided to aid further research of the subject.Strict Convexity and Complex Strict Convexity is essential fot mathematicians and studentsinterested in geometric theory of Banach spaces and applications to approximationtheory and fixed point theory, and is of great value to engineers working in optimizationstudies. In addition, this volume serves as an excellent text for a graduate course inGeometric Theory of Banach Spaces
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Stochastic Integration in Banach Spaces

Theory and Applications

Author: Vidyadhar Mandrekar,Barbara Rüdiger

Publisher: Springer

ISBN: 3319128531

Category: Mathematics

Page: 211

View: 2527

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​
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Geometric Aspects of Probability Theory and Mathematical Statistics

Author: V.V. Buldygin,A.B. Kharazishvili

Publisher: Springer Science & Business Media

ISBN: 9780792364139

Category: Mathematics

Page: 303

View: 4381

This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.
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Mathematics of Neural Networks

Models, Algorithms and Applications

Author: Stephen W. Ellacott,John C. Mason,Iain J. Anderson

Publisher: Springer Science & Business Media

ISBN: 9780792399339

Category: Computers

Page: 403

View: 386

This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.
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Weak Convergence of Measures

Applications in Probability

Author: Patrick Billingsley

Publisher: SIAM

ISBN: 0898711762

Category: Mathematics

Page: 31

View: 8329

A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.
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International Mathematical News

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2295

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
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Probability and Banach Spaces

Proceedings of a Conference Held in Zaragoza, Spain, June 17-21, 1985

Author: Jesús Bastero,Miguel San Miguel

Publisher: Springer

ISBN: N.A

Category: Banach spaces

Page: 222

View: 9487

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High Dimensional Probability VI

The Banff Volume

Author: Christian Houdré,David M. Mason,Jan Rosiński,Jon A. Wellner

Publisher: Springer Science & Business Media

ISBN: 3034804903

Category: Mathematics

Page: 374

View: 3494

This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. 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 areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.​
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