Download or read book Probability in Banach Spaces written by Michel Ledoux and published by Springer Science & Business Media. This book was released on 1991 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability Distributions on Banach Spaces written by N Vakhania and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability in Banach Spaces 8 Proceedings of the Eighth International Conference written by R.M. Dudley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability in Banach Spaces 9 written by Jorgen Hoffmann-Jorgensen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Martingales in Banach Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2016-06-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Download or read book Probability in Banach Spaces written by Anatole Beck and published by Springer. This book was released on 2006-11-14 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2018-02-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability in Banach Spaces V written by Anatole Beck and published by Springer. This book was released on 2006-11-14 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability in Banach Spaces written by Michel LeDoux and published by Springer. This book was released on 2014-01-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Banach Space Theory written by Marián Fabian and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Banach Spaces Analysis and Probability written by Daniel Li and published by Cambridge University Press. This book was released on 2018 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.
Download or read book Geometrical and Statistical Aspects of Probability in Banach Spaces written by Xavier Fernique and published by Springer. This book was released on 2006-11-14 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability in Banach Spaces 7 written by Eberlein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometry and Probability in Banach Spaces written by L. Schwartz and published by Springer. This book was released on 2006-11-14 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability in Banach Spaces 9 written by Jorgen Hoffmann-Jorgensen and published by Birkhäuser. This book was released on 1994-08-01 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Volume of Convex Bodies and Banach Space Geometry written by Gilles Pisier and published by Cambridge University Press. This book was released on 1999-05-27 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
