Conditional Measures and Applications
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Table of contents: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.This reference and text offers a thorough analysis of conditional expectations and probability measures, and demonstrat...
Table of contents:
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.
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.
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.
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.