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Convergence of Probability Measures

1999-07-30 Mathematics
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Release : 1999-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 454/5 ( 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 1999-07-30. 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.

Weak Convergence of Measures

1971-06-01 Mathematics
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Release : 1971-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 762/5 ( 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 1971-06-01. 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.

Probability and Measure

1986-01-17 Mathematics
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Release : 1986-01-17
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Probability and Measure by : Patrick Billingsley

Download or read book Probability and Measure written by Patrick Billingsley. This book was released on 1986-01-17. Available in PDF, EPUB and Kindle. Book excerpt: A senior-graduate level text and reference that links the disciplines of probability and measure theory. Including many practical problems and examples, it begins with an introduction to Borel's normal number theorem, proved by calculus alone, followed by short sections that establish the existence and fundamental properties of probability measures, including Lebesque measure on the unit interval. Coverage includes topics in measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes.

Probability Measures on Semigroups

2010-11-02 Mathematics
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Release : 2010-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 48X/5 ( reviews)

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Book Synopsis Probability Measures on Semigroups by : Göran Högnäs

Download or read book Probability Measures on Semigroups written by Göran Högnäs. This book was released on 2010-11-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability and Measure

2017
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Release : 2017
Genre :
Kind : eBook
Book Rating : 718/5 ( reviews)

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Book Synopsis Probability and Measure by : Patrick Billingsley

Download or read book Probability and Measure written by Patrick Billingsley. This book was released on 2017. 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

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