Probability In Banach Spaces

Probability in Banach Spaces PDF
Author: Michel Ledoux
Publisher: Springer Science & Business Media
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 493
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Book Description: 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 In Banach Spaces 9

Probability in Banach Spaces  9 PDF
Author: Jorgen Hoffmann-Jorgensen
Publisher: Springer Science & Business Media
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 422
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Book Description: 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 8 Proceedings Of The Eighth International Conference

Probability in Banach Spaces  8  Proceedings of the Eighth International Conference PDF
Author: R.M. Dudley
Publisher: Springer Science & Business Media
Format: PDF
Category : Mathematics
Languages : en
Pages : 512
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Book Description: 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

Probability in Banach Spaces PDF
Author: Michel LeDoux
Publisher: Springer
Format: PDF, ePub, Docs
Category :
Languages : en
Pages : 500
View: 4471
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Book Description: 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.


Probability In Banach Spaces

Probability in Banach Spaces PDF
Author: Anatole Beck
Publisher: Springer
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 291
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Probability In Banach Spaces

Probability in Banach Spaces PDF
Author: Michel Ledoux
Publisher:
Format: PDF
Category : Banach spaces
Languages : en
Pages : 480
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Probability In Banach Spaces V

Probability in Banach Spaces V PDF
Author: Anatole Beck
Publisher: Springer
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 463
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Probability In Banach Spaces

Probability in Banach Spaces PDF
Author: Michel Ledoux
Publisher:
Format: PDF, Mobi
Category : Banach spaces
Languages : en
Pages : 480
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Probability In Banach Spaces 7

Probability in Banach Spaces 7 PDF
Author: Eberlein
Publisher: Springer Science & Business Media
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 308
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Book Description: 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.


Probability In Banach Spaces 9

Probability in Banach Spaces  9 PDF
Author: Jorgen Hoffmann-Jorgensen
Publisher: Birkhäuser
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 431
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Book Description: 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.


Geometrical And Statistical Aspects Of Probability In Banach Spaces

Geometrical and Statistical Aspects of Probability in Banach Spaces PDF
Author: Xavier Fernique
Publisher: Springer
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 133
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Geometry And Probability In Banach Spaces

Geometry and Probability in Banach Spaces PDF
Author: L. Schwartz
Publisher: Springer
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 110
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Probability In Banach Spaces Iii

Probability in Banach Spaces III PDF
Author: A. Beck
Publisher: Springer
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 337
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Probability In Banach Spaces V

Probability in Banach Spaces V PDF
Author: Anatole Beck
Publisher:
Format: PDF, ePub, Mobi
Category :
Languages : en
Pages : 468
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Probability In Banach Spaces

Probability in Banach Spaces PDF
Author: Anatole Beck
Publisher:
Format: PDF, Docs
Category : Banach spaces
Languages : en
Pages :
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Probability In Banach Spaces 6

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Author: Haagerup
Publisher: Springer Science & Business Media
Format: PDF
Category : Mathematics
Languages : en
Pages : 298
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Book Description: This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was ar ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material pre sented in the lectures; several results covered have been published else where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these institu tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces. . . . .


Probability In Banach Spaces Ii

Probability in Banach Spaces II PDF
Author: A. Beck
Publisher:
Format: PDF
Category :
Languages : en
Pages : 220
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Probability And Banach Spaces

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Author: Jesus Bastero
Publisher:
Format: PDF
Category :
Languages : en
Pages : 246
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Probability In Banach Spaces Iv

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Author: A. Beck
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Format: PDF, Mobi
Category :
Languages : en
Pages : 244
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Probability In Banach Spaces Iv

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Author: A. Beck
Publisher: Lecture Notes in Mathematics
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 258
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Book Description: a