Conditional measures and applications
著者
書誌事項
Conditional measures and applications
（Monographs and textbooks in pure and applied mathematics, 177）
Marcel Dekker, c1993
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注記
Includes bibliographical references and index
Series on cover: Pure and applied mathematics : a series of monographs and textbooks
内容説明・目次
内容説明
This reference and text offers a thorough analysis of conditional expectations and probability measures, and demonstrates their important uses in real situations. Coverage includes applications to sufficiency, Markov processes, Martingales and analysis problems.;Presenting different characterizations of conditional operators and meausures to illuminate the abstract and functional analytic nature of conditioning, this volume: reviews the general concept of conditioning; supplies Kolmogorov's formulation and its properties; provides an axiomatic method for simplifying problems as an abstraction of Kolmogorov's general formulation; explicates sufficient statistics; and illustrates difficulties in the calculation of conditional expectations for continuous multivariate distributions and provides methods for correct solutions in many cases.;This work is designed as a reference for pure and applied mathematicians, probabilists, statisticians, information theorists, physicists and communication and industrial engineers; as well as a text for graduate level students in these discipines.
目次
- 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 of martingales and Markov processes
- applications to modern analysis
- conditioning in general structures
- references
- some frequently-used symbols.
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