Probability Theory, An Analytic View - Softcover

Stroock, Daniel W.

Softcover

ISBN 10: 1009549006 ISBN 13: 9781009549004

Publisher: Cambridge University Press, 2024

Synopsis

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.

About this title

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).

Edition details

• Publisher: Cambridge University Press
• Publication date: 2024
• Language: English
• ISBN 10: 1009549006
• ISBN 13: 9781009549004
• Binding: Paperback
• Edition number: 3
• Number of pages: 468