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Probability Theory, An Analytic View. 3rd Revised edition.
・ISBN 978-1-009-54900-4 paper GB£ 49.99
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お気に入り
★★★
電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-54903-5
| 著者・編者 | Stroock, Daniel W., |
|---|---|
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2024 |
| ページ数 | 466 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-13347＞ |
解説
The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies. The main changes are the inclusion of the Gaussian isoperimetric inequality plus many improvements and clarifications throughout the text. With more than 750 exercises, it is ideal for first-year graduate students with a good grasp of undergraduate probability theory and analysis. Starting with results about independent random variables, the author introduces weak convergence of measures and its application to the central limit theorem, and infinitely divisible laws and their associated stochastic processes. Conditional expectation and martingales follow before the context shifts to infinite dimensions, where Gaussian measures and weak convergence of measures are studied. The remainder is devoted to the mutually beneficial connection between probability theory and partial differential equations, culminating in an explanation of the relationship of Brownian motion to classical potential theory.