Convergence Of Probability Measures
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Convergence Of Probability Measures
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Author : Patrick Billingsley
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-25
Convergence Of Probability Measures written by Patrick Billingsley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-25 with Mathematics categories.
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.
Weak Convergence Of Measures
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Author : Patrick Billingsley
language : en
Publisher: SIAM
Release Date : 1971-01-01
Weak Convergence Of Measures written by Patrick Billingsley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.
A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.
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.
Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: David Pollard
Release Date : 1984-10-08
Convergence Of Stochastic Processes written by D. Pollard and has been published by David Pollard this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-08 with Mathematics categories.
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Probability And Measure
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Author : Patrick Billingsley
language : en
Publisher: John Wiley & Sons
Release Date : 2012-01-20
Probability And Measure written by Patrick Billingsley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-20 with Mathematics categories.
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including: An improved treatment of Brownian motion Replacement of queuing theory with ergodic theory Theory and applications used to illustrate real-life situations Over 300 problems with corresponding, intensive notes and solutions Updated bibliography An extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.
Weak Convergence Of Measures
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Author : Harald Bergström
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Weak Convergence Of Measures written by Harald Bergström and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Weak Convergence of Measures provides information pertinent to the fundamental aspects of weak convergence in probability theory. This book covers a variety of topics, including random variables, Hilbert spaces, Gaussian transforms, probability spaces, and random variables. Organized into six chapters, this book begins with an overview of elementary fundamental notions, including sets, different classes of sets, different topological spaces, and different classes of functions and measures. This text then provides the connection between functionals and measures by providing a detailed introduction of the abstract integral as a bounded, linear functional. Other chapters consider weak convergence of sequences of measures, such as convergence of sequences of bounded, linear functionals. This book discusses as well the weak convergence in the C- and D-spaces, which is reduced to limit problems. The final chapter deals with weak convergence in separable Hilbert spaces. This book is a valuable resource for mathematicians.
Stable Convergence And Stable Limit Theorems
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Author : Erich Häusler
language : en
Publisher: Springer
Release Date : 2015-06-09
Stable Convergence And Stable Limit Theorems written by Erich Häusler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-09 with Mathematics categories.
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Random Probability Measures On Polish Spaces
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Author : Hans Crauel
language : en
Publisher: CRC Press
Release Date : 2002-07-25
Random Probability Measures On Polish Spaces written by Hans Crauel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.
In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the rando
Probability Measures On Semigroups
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Author : Göran Högnäs
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02
Probability Measures On Semigroups written by Göran Högnäs 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 2010-11-02 with Mathematics categories.
This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.
A Weak Convergence Approach To The Theory Of Large Deviations
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Author : Paul Dupuis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
A Weak Convergence Approach To The Theory Of Large Deviations written by Paul Dupuis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.