Conditional measures and applications
著者
書誌事項
Conditional measures and applications
（Monographs and textbooks in pure and applied mathematics, 271）
Chapman & Hall/CRC, Taylor & Francis Group, 2005
2nd ed
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注記
Previous ed.: c1993
Includes bibliographical references (p. 455-470) and indexes
内容説明・目次
内容説明
In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and mere chapters in larger works on probability. This second edition continues to offer a thorough treatment of conditioning while adding substantial new information on developments and applications that have emerged over the past decade.
Conditional Measures and Applications, Second Edition clearly elucidates the subject, from fundamental principles to abstract analysis. The author illustrates the computational difficulties in evaluating conditional probabilities in nondiscrete cases with numerous examples, demonstrates applications to Markov processes, martingales, potential theory, and Reynolds operators as well as sufficiency in statistics, and clarifies ideas in modern noncommutative probability structures through conditioning in general structures, including parts of operator algebras and "free" random variables. He also discusses existence and construction problems from the Bishop-Brouwer constructive analysis point of view.
With open problems in every chapter and links to other areas of mathematics, this invaluable second edition offers complete coverage of conditional probability and expectation and their structural analysis, from simple to advanced abstract levels, for both novices and seasoned mathematicians.
目次
Preface to the Second Edition. Preface to the First Edition. The Concept of Conditioning. The Kolmogorov Formulation and Its Properties. Computational Problems Associated with Conditioning. An Axiomatic Approach to Conditional Probability. Regularity of Conditional Measures. Sufficiency. Abstraction of Kolmogorov's Formulation. Products of Conditional Measures. Applications to Martingales and Markov Processes. Applications to Modern Analysis. Conditioning in General Structures. References. Notations. Author Index. Subject Index.
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