High Dimensional Probability Vii

Author : Christian Houdré,David M. Mason,Patricia Reynaud-Bouret,Jan Rosiński
Publisher : Birkhäuser
Page : 480 pages
File Size : 42,9 Mb
Release : 2016-09-21
Category : Mathematics
ISBN : 9783319405193

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High Dimensional Probability VII by Christian Houdré,David M. Mason,Patricia Reynaud-Bouret,Jan Rosiński Pdf

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.

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 52,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author : Evarist Giné,David M. Mason,Jon A. Wellner
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213581

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High Dimensional Probability II by Evarist Giné,David M. Mason,Jon A. Wellner Pdf

High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.

Author : Radosław Adamczak,Nathael Gozlan,Karim Lounici,Mokshay Madiman
Publisher : Springer Nature
Page : 445 pages
File Size : 45,6 Mb
Release : 2023-06-05
Category : Mathematics
ISBN : 9783031269790

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High Dimensional Probability IX by Radosław Adamczak,Nathael Gozlan,Karim Lounici,Mokshay Madiman Pdf

This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.

Author : Joergen Hoffmann-Joergensen,Michael B. Marcus,Jon A. Wellner
Publisher : Birkhäuser
Page : 346 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880596

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High Dimensional Probability III by Joergen Hoffmann-Joergensen,Michael B. Marcus,Jon A. Wellner Pdf

The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. The volume thus will be a valuable resource for postgraduates and reseachers in probability theory and mathematical statistics.

Author : Ernst Eberlein,Marjorie Hahn
Publisher : Birkhäuser
Page : 336 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888295

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High Dimensional Probability by Ernst Eberlein,Marjorie Hahn Pdf

What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.

Author : Evarist Giné
Publisher : IMS
Page : 288 pages
File Size : 44,9 Mb
Release : 2006
Category : Mathematics
ISBN : 0940600676

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High Dimensional Probability by Evarist Giné Pdf

Author : Jørgen Hoffmann-Jørgensen,Michael B. Marcus,Jon A. Wellner
Publisher : Birkhauser
Page : 346 pages
File Size : 43,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0817621873

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High Dimensional Probability III by Jørgen Hoffmann-Jørgensen,Michael B. Marcus,Jon A. Wellner Pdf

Author : Eric Carlen,Mokshay Madiman,Elisabeth M. Werner
Publisher : Springer
Page : 626 pages
File Size : 55,6 Mb
Release : 2017-04-20
Category : Mathematics
ISBN : 9781493970056

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Convexity and Concentration by Eric Carlen,Mokshay Madiman,Elisabeth M. Werner Pdf

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.

Author : Michel Talagrand
Publisher : Springer Nature
Page : 727 pages
File Size : 43,8 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030825959

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Upper and Lower Bounds for Stochastic Processes by Michel Talagrand Pdf

This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist’s toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author’s influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.

Author : Christian Houdré,David M. Mason,Jan Rosiński,Jon A. Wellner
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 47,6 Mb
Release : 2013-04-19
Category : Mathematics
ISBN : 9783034804905

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High Dimensional Probability VI by Christian Houdré,David M. Mason,Jan Rosiński,Jon A. Wellner Pdf

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.​

Author : Laurent Decreusefond,Bernt Oksendal,Ali S. Üstünel
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201571

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Stochastic Analysis and Related Topics VII by Laurent Decreusefond,Bernt Oksendal,Ali S. Üstünel Pdf

One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.

Author : María Cristina Pereyra,Stefania Marcantognini,Alexander M. Stokolos,Wilfredo Urbina
Publisher : Springer
Page : 371 pages
File Size : 45,8 Mb
Release : 2016-09-15
Category : Mathematics
ISBN : 9783319309613

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Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1) by María Cristina Pereyra,Stefania Marcantognini,Alexander M. Stokolos,Wilfredo Urbina Pdf

Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed, high-quality papers exploring new results and trends in spectral theory, mathematical physics, geometric function theory, and partial differential equations. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. Another shared research interest of the contributors of this volume lies in the area of applied harmonic analysis, where a new notion called chromatic derivatives has recently been introduced in communication engineering. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6, 2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional mathematician and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.

Author : Anonim
Publisher : Unknown
Page : 275 pages
File Size : 46,7 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:1132151423

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High Dimensional Probability by Anonim Pdf

Author : Victor M. Panaretos,Yoav Zemel
Publisher : Springer Nature
Page : 157 pages
File Size : 41,8 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9783030384388

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An Invitation to Statistics in Wasserstein Space by Victor M. Panaretos,Yoav Zemel Pdf

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.