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.

Im Mittelpunkt dieses Buches stehen langsam konvergierende Methoden in metrischen Rumen, deren Fhigkeiten und Nutzen anhand zahlreicher Beispiele vorgefhrt werden. Die berarbeitete 2. Auflage enthlt jetzt auch Angaben zu Unterrumen, dem Skorohodschen Darstellungstheorem, der Prohorov-Metrik und dem Poisson-Limit. (09/99)