Convergence of Probability Measures
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Beschreibung
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 Räumen, deren Fähigkeiten und Nutzen anhand zahlreicher Beispiele vorgeführt werden. Die überarbeitete 2. Auflage enthält jetzt auch Angaben zu Unterräumen, dem Skorohodschen Darstellungstheorem, der Prohorov-Metrik und dem Poisson-Limit. (09/99)
Autor*in
Patrick Billingsley
Themen in »Convergence of Probability Measures«
Konvergenz (Math.) Metrischer Raum Probability & Mathematical Statistics Statistics Statistik Wahrscheinlichkeitsrechnung u. mathematische Statistik
Stimmen zu »Convergence of Probability Measures«
The book is a classic [...]. (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)
"...the author may be congratulated. The book will definitely maintain and extend its role as a fundamental introduction and contribution to the subject." (Statistics & Decisions, Vol. 18/3, 2000)
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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)
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