Probability Theory, An Analytic View
Probability Theory, An Analytic View
£49.99
GBPThe 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.
- Provides and explains the connections between probability theory and other branches of analysis
- Contains material not readily accessible elsewhere
- Thoroughly updated with new material including a section on isoperimetric inequality
Product details
November 2024Paperback
9781009549004
466 pages
254 × 177 × 25 mm
0.85kg
Available
Table of Contents
- Notation
- 1. Sums of independent random variables
- 2. The central limit theorem
- 3. Infinitely divisible laws
- 4. Lé vy 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.
