Convergence Of Probability Measures

Author : Patrick Billingsley
Publisher : John Wiley & Sons
ISBN 13 : 111862596X
Total Pages : 253 pages
Book Rating : 4.65/5 ( download)

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Download or read book Convergence of Probability Measures written by Patrick Billingsley and published by John Wiley & Sons. This book was released on 2013-06-25 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Patrick Billingsley
Publisher : SIAM
ISBN 13 : 9781611970623
Total Pages : 37 pages
Book Rating : 4.28/5 ( download)

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Download or read book Weak Convergence of Measures written by Patrick Billingsley and published by SIAM. This book was released on 1971-01-01 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Patrick Billingsley
Publisher : John Wiley & Sons
ISBN 13 : 9788126517718
Total Pages : 612 pages
Book Rating : 4.19/5 ( download)

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Download or read book Probability and Measure written by Patrick Billingsley and published by John Wiley & Sons. This book was released on 2017 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

Author : Paul Dupuis
Publisher : John Wiley & Sons
ISBN 13 : 1118165896
Total Pages : 506 pages
Book Rating : 4.98/5 ( download)

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Download or read book A Weak Convergence Approach to the Theory of Large Deviations written by Paul Dupuis and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147044738X
Total Pages : 286 pages
Book Rating : 4.80/5 ( download)

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Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : D. Pollard
Publisher : David Pollard
ISBN 13 : 0387909907
Total Pages : 223 pages
Book Rating : 4.05/5 ( download)

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Download or read book Convergence of Stochastic Processes written by D. Pollard and published by David Pollard. This book was released on 1984-10-08 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : H. Heyer
Publisher : Springer Science & Business Media
ISBN 13 : 3642667066
Total Pages : 542 pages
Book Rating : 4.60/5 ( download)

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Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Author : Hans Crauel
Publisher : CRC Press
ISBN 13 : 1134480377
Total Pages : 186 pages
Book Rating : 4.71/5 ( download)

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Download or read book Random Probability Measures on Polish Spaces written by Hans Crauel and published by CRC Press. This book was released on 2002-07-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : R. M. Dudley
Publisher : Cambridge University Press
ISBN 13 : 9780521007542
Total Pages : 570 pages
Book Rating : 4.42/5 ( download)

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Download or read book Real Analysis and Probability written by R. M. Dudley and published by Cambridge University Press. This book was released on 2002-10-14 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text offers a clear exposition of modern probability theory.

Author : K.R. Parthasarathy
Publisher : Springer
ISBN 13 : 9386279274
Total Pages : 352 pages
Book Rating : 4.79/5 ( download)

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Download or read book Introduction to Probability and Measure written by K.R. Parthasarathy and published by Springer. This book was released on 2005-05-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account.