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Convergence of Probability Measures, 2nd Edition

Convergence of Probability Measures, 2nd Edition

Patrick Billingsley

ISBN: 978-0-471-19745-4 August 1999 296 Pages


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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 in Metric Spaces.

The Space C.

The Space D.

Dependent Variables.

Other Modes of Convergence.


Some Notes on the Problems.

Bibliographical Notes.


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) 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)