Convergence of Probability Measures
Wiley Series in Probability and Statistics
2. Edition August 1999
304 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Asymptotic distribution theorems in probability and statistics have, from the beginning, depended on the classical theory of weak convergence of distribution functions in Euclidean space. The past several decades have seen the creation and extensive application of a more inclusive theory of weak convergence of probability measures on metric spaces. There are many asymptotic results that can be formulated within the classical theory but require for their proofs this more general theory, which thus does not merely study itself. Written by a well-know and respected expert in the field, this book is about weak convergence methods in metric spaces, with applications sufficient to show their power and utility.
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.
The Space C.
The Space D.
Dependent Variables.
Other Modes of Convergence.
Appendix.
Some Notes on the Problems.
Bibliographical Notes.
Bibliography.
Index.
...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)
