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Probability in Banach Spaces

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
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Book Rating : 128/5 ( reviews)

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Book Synopsis Probability in Banach Spaces by : Michel Ledoux

Download or read book Probability in Banach Spaces written by Michel Ledoux. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability Distributions on Banach Spaces

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 73X/5 ( reviews)

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Book Synopsis Probability Distributions on Banach Spaces by : N Vakhania

Download or read book Probability Distributions on Banach Spaces written by N Vakhania. This book was released on 2012-12-06. 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.

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

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 678/5 ( reviews)

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Book Synopsis Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference by : R.M. Dudley

Download or read book Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference written by R.M. Dudley. This book was released on 2012-12-06. 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.

Probability in Banach Spaces, 9

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 531/5 ( reviews)

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Book Synopsis Probability in Banach Spaces, 9 by : Jorgen Hoffmann-Jorgensen

Download or read book Probability in Banach Spaces, 9 written by Jorgen Hoffmann-Jorgensen. This book was released on 2012-12-06. 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.

Probability in Banach Spaces

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
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Book Rating : 569/5 ( reviews)

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Book Synopsis Probability in Banach Spaces by : Anatole Beck

Download or read book Probability in Banach Spaces written by Anatole Beck. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt:

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