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<図書>
A user's guide to measure theoretic probability

責任表示 David Pollard
シリーズ Cambridge series on statistical and probabilistic mathematics
データ種別 図書
出版者 Cambridge : Cambridge University Press
出版年 2002
本文言語 英語
大きさ xiii, 351 p. : ill. ; 26 cm
概要 This book grew from a need to teach a rigorous probability course to a mixed audience - statisticians, mathematically inclined biostatisticians, mathematicians, economists, and students of finance - a... the advanced undergraduate/introductory graduate level, without the luxury of a course in measure theory as a prerequisite. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition, there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and Fernique's inequality for Gaussian processes. In a further break with tradition, the necessary measure theory is developed via the identification of integrals with linear functionals on spaces of measurable functions, allowing quicker access to the full power of the measure theoretic methods. The book is not just a presentation of mathematically rigorous theory; it is also a discussion of why some of that theory takes its current form and how anyone could have thought of those clever ideas in the first place. It is intended as a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and to understand what they mean. Book jacket.
This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
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所蔵情報


理系図3F 数理独自 023212001008158 POLL/20/3 2002

理系図3F 数理独自 023212009002686 POLL/20/3A 2002

書誌詳細

一般注記 Includes bibliographical references and index
著者標目 *Pollard, David, 1950-
件 名 LCSH:Probabilities
LCSH:Measure theory
分 類 LCC:QA273
DC21:519.2
書誌ID 1001238562
ISBN 0521802423
NCID BA55578546
巻冊次 ISBN:0521802423
: pbk ; ISBN:0521002893
登録日 2009.09.18
更新日 2009.11.02

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