
Probability Theory, An Analytic View
Daniel W. Stroock(Author)
Cambridge University Press
3rd Edition
Published on 21. November 2024
Book
Paperback/Softback
466 pages
978-1-009-54900-4 (ISBN)
Description
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.
More details
Edition
3rd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 26 mm
Weight
873 gr
ISBN-13
978-1-009-54900-4 (9781009549004)
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Schweitzer Classification
Other editions
Previous edition

Book
12/2010
2nd Edition
Cambridge University Press
€134.86
Article exhausted; check for reprint
Person
Daniel W. Stroock is Simons Professor Emeritus of Mathematics at the Massachusetts Institute of Technology. He has published numerous articles and books, most recently 'Elements of Stochastic Calculus and Analysis' (2018) and 'Gaussian Measures in Finite and Infinite Dimensions' (2023).
Content
Notation; 1. Sums of independent random variables; 2. The central limit theorem; 3. Infinitely divisible laws; 4. Levy processes; 5. Conditioning and martingales; 6. Some extensions and applications of martingale theory; 7. Continuous parameter martingales; 8. Gaussian measures on a Banach space; 9. Convergence of measures on a Polish space; 10. Wiener measure and partial differential equations; 11. Some classical potential theory; References; Index.