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Synopsis
This revised edition is suitable for a first-year graduate course on probability theory. It is intended for students with a good grasp of introductory, undergraduate probability and a reasonably sophisticated introduction to modern analysis who now want to learn what these two topics have to say about each other. By modern standards the topics treated here are classical and the techniques used far-ranging. No attempt has been made to present the subject as a monolithic structure resting on a few basic principles. The first part of the book deals with independent random variables, Central Limit phenomena, the general theory of weak convergence and several of its applications, as well as elements of both the Gaussian and Markovian theory of measures on function space. The introduction of conditional expectation values is postponed until the second part of the book where it is applied to the study of martingales. This section also explores the connection between martingales and various aspects of classical analysis and the connections between Wiener's measure and classical potential theory.
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Book Description
This revised edition is suitable for a first-year graduate course on probability theory. It is intended for students with a good grasp of undergraduate probability and a reasonably sophisticated introduction to modern analysis who now want to learn what these two topics have to say about each other. It will also be a valuable reference for those in fields as diverse as physics, engineering, and economics.
Review
..".a first-class work of reference, for technique as well as for results and definitve theory; even as extended a review as this does not do justice to its detail and density." Peter Whittle, The Mathematical Intelligencer
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- PublisherCambridge University Press
- Publication date1994
- ISBN 10 0521431239
- ISBN 13 9780521431231
- BindingHardcover
- LanguageEnglish
- Number of pages528
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Probability Theory, an Analytic View
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Cambridge University Press, 1994
ISBN 10: 0521431239
ISBN 13: 9780521431231
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Probability Theory, an Analytic View
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ISBN 10: 0521431239
ISBN 13: 9780521431231
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Probability Theory, an Analytic View
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ISBN 13: 9780521431231
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Probability Theory. An Analytic View.
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Probability Theory, an Analytic View
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ISBN 10: 0521431239
ISBN 13: 9780521431231
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