Convergence of Probability Measures
By: Patrick Billingsley.
Edition: 2nd ed.
Series: Wiley Series in Probability and Statistics: Probability and Statistics Section
Publisher: Wiley-Interscience
Published: 1999
Place of publication: New York, USA
Language: eng
Format: Hardcover
Number of pages: 277
ISBN-13: 9780471197454
Copyright date: 1999
Subjects: Probability measures; Metric spaces; Convergence
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.
--back cover
Notes: Includes bibliographical references (p. 270-274) and indexes.
Table of contents: title: Ch. 1. Weak Convergence in Metric Spaces --; title: Sect. 1. Measures on Metric Spaces --; title: Sect. 2. Properties of Weak Convergence --; title: Sect. 3. Convergence in Distribution --; title: Sect. 4. Long Cycles and Large Divisors --; title: Sect. 5. Prohorov's Theorem --; title: Sect. 6. A Miscellany --; title: Ch. 2. The Space C --; title: Sect. 7. Weak Convergence and Tightness in C --; title: Sect. 8. Wiener Measure and Donsker's Theorem --; title: Sect. 9. Functions of Brownian Motion Paths --; title: Sect. 10. Maximal Inequalities --; title: Sect. 11. Trigonometric Series --; title: Ch. 3. The Space D --; title: Sect. 12. The Geometry of D --; title: Sect. 13. Weak Convergence and Tightness in D --; title: Sect. 14. Applications --; title: Sect. 15. Uniform Topologies --; title: Sect. 16. The Space D(0, [infinity]) --; title: Ch. 4. Dependent Variables --; title: Sect. 17. More on Prime Divisors --; title: Sect. 18. Martingales --; title: Sect. 19. Ergodic Processes --; title: Ch. 5. Other Modes of Convergence --; title: Sect. 20. Convergence in Probability --; title: Sect. 21. Approximation by Independent Normal Sequences --; title: Sect. 22. Strassen's Theorem --; title: App. M. Metric Spaces. Analysis. Convexity. Probability.