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Weak Convergence of Measures

2014-05-10 Mathematics
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Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 451/5 ( reviews)

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Book Synopsis Weak Convergence of Measures by : Harald Bergström

Download or read book Weak Convergence of Measures written by Harald Bergström. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Weak Convergence of Measures

1971-01-01 Mathematics
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Release : 1971-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 623/5 ( reviews)

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Book Synopsis Weak Convergence of Measures by : Patrick Billingsley

Download or read book Weak Convergence of Measures written by Patrick Billingsley. This book was released on 1971-01-01. 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.

Weak Convergence of Measures

2018-09-27 Mathematics
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Release : 2018-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 38X/5 ( reviews)

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Book Synopsis Weak Convergence of Measures by : Vladimir I. Bogachev

Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev. This book was released on 2018-09-27. 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.

Convergence of Probability Measures

2013-06-25 Mathematics
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Release : 2013-06-25
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)

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Book Synopsis Convergence of Probability Measures by : Patrick Billingsley

Download or read book Convergence of Probability Measures written by Patrick Billingsley. This book was released on 2013-06-25. 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.

A Weak Convergence Approach to the Theory of Large Deviations

2011-09-09 Mathematics
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Release : 2011-09-09
Genre : Mathematics
Kind : eBook
Book Rating : 896/5 ( reviews)

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Book Synopsis A Weak Convergence Approach to the Theory of Large Deviations by : Paul Dupuis

Download or read book A Weak Convergence Approach to the Theory of Large Deviations written by Paul Dupuis. This book was released on 2011-09-09. 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.

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