Publisher finelybook 出版社:Cambridge University Press
Edition 版次: 3rd edition
Publication Date 出版日期: November 21, 2024
Language 语言: English
Print Length 页数: 466 pages
ISBN-10: 1009549006
ISBN-13: 9781009549004
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.
Book Description
By finelybook
A rigorous, yet entertaining, account of the analytic foundations on which Kolmogorov built the theory of probability.
About the Author
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).
