Convergence of Probability Measures 2nd Edition by Patrick Billingsley (PDF)

Description

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.

User’s Reviews

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 Inside Flap 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. 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. About the Author PATRICK BILLINGSLEY, PhD, is Professor of Mathematics and Statistics at the University of Chicago. His book, Probability and Measure, Third Edition, is also available from Wiley. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is what made “popular” this area of probability. They key results in this area date back to the mid 1950’s and this book appeared in 1968. It is an excellent book and in the 2nd edition it has been updated to bring the coverage closer to the way topics are treated in research; in particular, it covers now convergence in D[0, infinity), necessary to deal with convergence of stochastic processes.It is more elementary than Jacod and Shiryaev’s Limit Theorems for Stochastic Processes, a book that deals with much more advanced topics and applications to start with and Billingsley’s is therefore more readable making it excellent to introduce advanced students to the subject.Billingsley provides a good collection of examples that increase the readability of the textbook and makes it easier for students to appreciateseveral of the technicalities.It is not an “easy” book and students must be willing to put a lot of hours and efforts into understanding the topics, but it is a rewarding book.

⭐If you are not doing research on relevant fields, don’t waste your money purchasing it.

⭐This is the Indian edition, which is apparently supposed to be sold only within India.

⭐It’s very good.

⭐Patrick Billingsley was my doctoral supervisor at the University of Chicago in the 1980s, and I worked through in detail the first edition of CONVERGENCE OF PROBABILITY MEASURES with him directly. The first edition was great, and I would give it five stars (unfortunately I can’t since it is not listed at Amazon).I always liked Patrick, and after he died I bought the second edition, but didn’t crack it open at the time — it was more a “homage purchase.” Recently, I’ve been going over Brownian motions in finance, and I thought I’d look at the second edition for its derivation of Brownian motion. As an exercise in nostalgia. I decided to start reading at the front of the second edition.WHAT A MESS! You’d think that with TeX the typesetting quality and the accuracy of the formulae would be improved. Not so. Example: If you happen to have the first and second editions, look at the bottom equation on p. 4 in the first edition and the top equation on p. 5 in the second edition. The equation in the first edition is correct. The equation in the second edition has not one but two errors (any one of which are fatal and confusing). The equations are supposed to be the same.As I was reading the second edition, I was asking myself how it could be that I found it so opaque and why it was failing to jog my memory. It’s as though at every point notations have been changed to make reading the book less comprehensible. For instance, the use of “S” for a metric space and script “S” for the associated Borel sets is crystal clear in the first edition –they look completely different there. In the second edition they look almost the same.If you want to know and appreciate why this book is a classic, get the first edition. There are copies available at Abebooks.

⭐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.

⭐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.

⭐Delivered on time and product as advertised

⭐The print is very bad, and I think it is just a version of Amazon not from Wiley.

⭐The publisher should really take more care of their books. The quality of this book really looks like some pirated book (even worse). After several days, the page is already loose I am sure pages will be split and fall down in a short time. The words on the paper are kind of blur, not comfortable to read. And now I have just read about the first 20 pages. There is already two 15-16 pages in the book..This is totally unacceptable.

⭐Me enviaron otro libro y jamás me proporcionar un transportista para devolver lo.

⭐

Keywords

Free Download Convergence of Probability Measures 2nd Edition in PDF format
Convergence of Probability Measures 2nd Edition PDF Free Download
Download Convergence of Probability Measures 2nd Edition 1974 PDF Free
Convergence of Probability Measures 2nd Edition 1974 PDF Free Download
Download Convergence of Probability Measures 2nd Edition PDF
Free Download Ebook Convergence of Probability Measures 2nd Edition