Probability theory, an analytic view
著者
書誌事項
Probability theory, an analytic view
Cambridge University Press, 1999 ,c1993
[revised ed.]
- : pbk
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注記
[revised edition] - on cover -
First paperback edition 1999
Includes index
内容説明・目次
内容説明
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 is a reasonably sophisticated introduction to modern analysis for those who want to learn what these two topics have to say about each other. 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.
目次
- 1. Sums of independent random variables
- 2. The central limit theorem
- 3. Convergence of measures, infinite divisibility, and processes with independent increments
- 4. A celebration of Wiener's measure
- 5. Conditioning and martingales
- 6. Some applications of martingale theory
- 7. Continuous martingales and elementary diffiusion theory
- 8. A little classical potential theory.
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