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Convergence of Probability Measures (Wiley Series in Probability and Mathematical Statistics) [Hardcover]

Patrick Billingsley
3.7 out of 5 stars  See all reviews (3 customer reviews)


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Convergence of Probability Measures Convergence of Probability Measures 3.7 out of 5 stars (3)
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Book Description

January 15, 1968 0471072427 978-0471072423 1
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.


Editorial Reviews

Review

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)

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.

Product Details

  • Series: Wiley Series in Probability and Mathematical Statistics (Book 9)
  • Hardcover: 272 pages
  • Publisher: Wiley; 1 edition (January 15, 1968)
  • Language: English
  • ISBN-10: 0471072427
  • ISBN-13: 978-0471072423
  • Product Dimensions: 9 x 6.1 x 0.7 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #3,307,774 in Books (See Top 100 in Books)

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Customer Reviews

3.7 out of 5 stars
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Most Helpful Customer Reviews
46 of 49 people found the following review helpful
5.0 out of 5 stars weak convergence taught rigorously April 7, 2008
Format: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.
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1.0 out of 5 stars Kindle version is a mess January 8, 2014
Format:Kindle Edition
While the book itself is a classic and the content deserves 5 stars, the Kindle version is a shipwreck.

Where to start? Displayed equations: they have just scanned the paper equations, cropped them and stuck them in with no regard for spacing between lines, with the equation number much lower than the vertical center of the equation. The resolution of these monstrosities varies considerably, from pin sharp to almost unreadably blurry.

Inline equations: they alter between the same cut-and-paste approach as above, so the equations are sometimes not centered vertically, or they convert the equations to text font, which usually works but sometimes not (eg you'll get "is a member of" instead of epsilon).

But the cherry on the cake is that they can't even get the text right. I've just read on a random page: "Either of ifie following conditions" instead of "Either of the following conditions...". On another page their is a missing "d" at the end of Skorohod.
These are from sections 15 and 16 which are particularly bad.

I'm astonished that someone decided it's acceptable to put this on the market, at any price. I'm getting a refund.
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9 of 25 people found the following review helpful
5.0 out of 5 stars THE BOOK on WEAK CONVERGENCE July 15, 1998
By A Customer
Format: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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