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.
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The book is a classic--it is almost an insult to review it. This second edition will, probably and rightly, be urged on today's research students by their predecessors, now their supervisors, who derived so much from the first edition. As the author says, 30 years ago the book would take the aspiring researcher to the forefront. Now, with the huge development over these years, it just provides an initial grounding, though no less essential. (The Statistician 49 (3) 2000)
...it seems destined to become another clasic and is of interest even to those who already own the first edition. (Zentralblatt Math, Volume 944, No 19, 2000)
...it seems destined to become another clasic and is of interest even to those who already own the first edition. (Zentralblatt Math, Volume 944, No 19, 2000)
From the Back Cover
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.
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45 of 47 people found the following review helpful:
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weak convergence taught rigorously,
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This review is from: Convergence of Probability Measures (Wiley Series in Probability and Statistics) (Hardcover)
When I was a graduate student at Stanford in the late 1970s I took a course in stochastic processes from Sid Resnick. Patrick Billingsley is an excellent probabilist who has written some very clear texts on probability theory and measure theory. In studying asymptotic distribution theory for independent or dependent data convergence in probability is a very important problem and Billingsley was the master at explaining it as well as the other major probability convergence criteria. So we relied heavily on Billingsley's two books on the convergence of probability measures. This text was in its first edition and was referred to as Big Bill because it was the more detailed of the two books. The other which came in paperback was simpler and more concise. That one we called Little Bill. Although we tended to find what we needed in Little Bill, Big Bill was useful also.
8 of 23 people found the following review helpful:
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THE BOOK on WEAK CONVERGENCE,
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This review is from: Convergence of Probability Measures (Wiley Series in Probability and Mathematical Statistics) (Hardcover)
A classic, will survive through the ages as long as Real Analysis and Probability are studied by students the world over. You need it to get a fundamental grounding in Probability Theory
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Inside This Book
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First Sentence:
The De Moivre-Laplace limit theorem says that, if is the distribution function of the normalized number of successes in n Bernoulli trials, and if is the standard normal distribution function, then for all x (the probability p of success fixed). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
separable support, random walk case, arc sine law, separating class, distinct prime divisors, mapping theorem, relative compactness, weak convergence, further subsequence, martingale difference, random element New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The De Moivre-Laplace limit theorem says that, if is the distribution function of the normalized number of successes in n Bernoulli trials, and if is the standard normal distribution function, then for all x (the probability p of success fixed). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
separable support, random walk case, arc sine law, separating class, distinct prime divisors, mapping theorem, relative compactness, weak convergence, further subsequence, martingale difference, random element New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
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- Probability and Measure, 3rd Edition by Patrick Billingsley in Back Matter (1), and Back Matter (2)
- Stochastic Processes (Wiley Classics Library) by J. L. Doob in Back Matter (1), and Back Matter (2)
- Order Statistics (Wiley Series in Probability and Statistics) by Herbert A. David in Back Matter (1), and Back Matter (2)
- Survey Measurement and Process Quality by Lars E. Lyberg in Back Matter
- The Statistical Analysis of Failure Time Data (Wiley Series in Probability and Statistics) by John D. Kalbfleisch in Back Matter
See all 100 books this book cites
- Time Series Analysis: Nonstationary and Noninvertible Distribution Theory (Wiley Series in Probability and Statistics) by Katsuto Tanaka on page 609, Back Matter (1), and Back Matter (2)
- Soft Methodology and Random Information Systems (Advances in Intelligent and Soft Computing) by Miguel Concepcion Lopez-Diaz on page 31, page 42, and page 84
- A Guide to Chi-Squared Testing (Wiley Series in Probability and Statistics) by Priscilla E. Greenwood in Back Matter (1), and Back Matter (2)
- Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons (Wiley Series in Probability and Statistics) by Robert E. Bechhofer in Back Matter (1), and Back Matter (2)
- Stochastic Analysis and Applications (Advances in Probability and Related Topics) by Pinsky Mark A on page 321, and page 437
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