Selected Works Of R M Dudley

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Selected Works Of R M Dudley

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Author : Evarist Giné
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-13

Selected Works Of R M Dudley written by Evarist Giné and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-13 with Mathematics categories.

For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. His work on Gaussian processes led to the understanding of the basic fact that their sample boundedness and continuity should be characterized in terms of proper measures of complexity of their parameter spaces equipped with the intrinsic covariance metric. His sufficient condition for sample continuity in terms of metric entropy is widely used and was proved by X. Fernique to be necessary for stationary Gaussian processes, whereas its more subtle versions (majorizing measures) were proved by M. Talagrand to be necessary in general. Together with V. N. Vapnik and A. Y. Cervonenkis, R. M. Dudley is a founder of the modern theory of empirical processes in general spaces. His work on uniform central limit theorems (under bracketing entropy conditions and for Vapnik-Cervonenkis classes), greatly extends classical results that go back to A. N. Kolmogorov and M. D. Donsker, and became the starting point of a new line of research, continued in the work of Dudley and others, that developed empirical processes into one of the major tools in mathematical statistics and statistical learning theory. As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm. In a further recent step Dudley replaces this norm by the stronger p-variation norms, which then allows replacing compact differentiability of many statistical functionals by Fréchet differentiability in the delta method. Richard M. Dudley has also made important contributions to mathematical statistics, the theory of weak convergence, relativistic Markov processes, differentiability of nonlinear operators and several other areas of mathematics. Professor Dudley has been the adviser to thirty PhD's and is a Professor of Mathematics at the Massachusetts Institute of Technology.

Selected Works Of R M Dudley

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Author : Evarist Giné
language : en
Publisher: Springer
Release Date : 2010-08-25

Selected Works Of R M Dudley written by Evarist Giné and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-25 with Mathematics categories.

For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. His work on Gaussian processes led to the understanding of the basic fact that their sample boundedness and continuity should be characterized in terms of proper measures of complexity of their parameter spaces equipped with the intrinsic covariance metric. His sufficient condition for sample continuity in terms of metric entropy is widely used and was proved by X. Fernique to be necessary for stationary Gaussian processes, whereas its more subtle versions (majorizing measures) were proved by M. Talagrand to be necessary in general. Together with V. N. Vapnik and A. Y. Cervonenkis, R. M. Dudley is a founder of the modern theory of empirical processes in general spaces. His work on uniform central limit theorems (under bracketing entropy conditions and for Vapnik-Cervonenkis classes), greatly extends classical results that go back to A. N. Kolmogorov and M. D. Donsker, and became the starting point of a new line of research, continued in the work of Dudley and others, that developed empirical processes into one of the major tools in mathematical statistics and statistical learning theory. As a consequence of Dudley's early work on weak convergence of probability measures on non-separable metric spaces, the Skorohod topology on the space of regulated right-continuous functions can be replaced, in the study of weak convergence of the empirical distribution function, by the supremum norm. In a further recent step Dudley replaces this norm by the stronger p-variation norms, which then allows replacing compact differentiability of many statistical functionals by Fréchet differentiability in the delta method. Richard M. Dudley has also made important contributions to mathematical statistics, the theory of weak convergence, relativistic Markov processes, differentiability of nonlinear operators and several other areas of mathematics. Professor Dudley has been the adviser to thirty PhD's and is a Professor of Mathematics at the Massachusetts Institute of Technology.

Brownian Motion

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Author : René L. Schilling
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-09-07

Brownian Motion written by René L. Schilling and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.

Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.

Selected Works Of Oded Schramm

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Author : Itai Benjamini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-12

Selected Works Of Oded Schramm written by Itai Benjamini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Mathematics categories.

This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.

Weak Convergence Of Measures

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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-27

Weak Convergence Of Measures written by Vladimir I. Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Convergence categories.

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

Selected Works Of Willem Van Zwet

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Author : Sara van de Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-21

Selected Works Of Willem Van Zwet written by Sara van de Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-21 with Mathematics categories.

With this collections volume, some of the important works of Willem van Zwet are moved to the front layers of modern statistics. The selection was based on discussions with Willem, and aims at a representative sample. The result is a collection of papers that the new generations of statisticians should not be denied. They are here to stay, to enjoy and to form the basis for further research. The papers are grouped into six themes: fundamental statistics, asymptotic theory, second-order approximations, resampling, applications, and probability. This volume serves as basic reference for fundamental statistical theory, and at the same time reveals some of its history. The papers are grouped into six themes: fundamental statistics, asymptotic theory, second-order approximations, resampling, applications, and probability. This volume serves as basic reference for fundamental statistical theory, and at the same time reveals some of its history.

Real Analysis And Probability

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Author : R. M. Dudley
language : en
Publisher: Cambridge University Press
Release Date : 2002-10-14

Real Analysis And Probability written by R. M. Dudley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-14 with Mathematics categories.

This classic text offers a clear exposition of modern probability theory.

Engineering Applications Of Neural Networks

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Author : Lazaros Iliadis
language : en
Publisher: Springer Nature
Release Date : 2023-06-06

Engineering Applications Of Neural Networks written by Lazaros Iliadis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Computers categories.

This book constitutes the refereed proceedings of the 24th International Conference on Engineering Applications of Neural Networks, EANN 2023, held in León, Spain, in June 2023. The 41 revised full papers and 8 revised short papers presented were carefully reviewed and selected from 125 submissions. The papers are organized in topical sections on ​artificial intelligence - computational methods - ethology; classification - filtering - genetic algorithms; complex dynamic networks' optimization/ graph neural networks; convolutional neural networks/spiking neural networks; deep learning modeling; deep/machine learning in engineering; LEARNING (reinforcemet - federated - adversarial - transfer); natural language - recommendation systems.

Uniform Central Limit Theorems

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Author : R. M. Dudley
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-28

Uniform Central Limit Theorems written by R. M. Dudley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-28 with Mathematics categories.

This treatise by an acknowledged expert includes several topics not found in any previous book.

Selected Papers On Probability And Statistics

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Selected Papers On Probability And Statistics written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.