Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- 1 Sums of Independent Random Variables
- 2 The Central Limit Theorem
- 3 Infinitely Divisible Laws
- 4 Lévy 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
9 - Convergence of Measures on a Polish Space
Published online by Cambridge University Press: 07 November 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- 1 Sums of Independent Random Variables
- 2 The Central Limit Theorem
- 3 Infinitely Divisible Laws
- 4 Lévy 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
Summary
The central topic here is the abstract theory of weak convergence of probability measures on a Polish space. The basic theory is developed in §9.1. In §9.2 I apply the theory to prove the existence of regular conditional probability distributions, and in §9.3 I use it to derive Donsker’s Invariance Principle (i.e., the pathspace statement of the Central Limit Theorem).
- Type
- Chapter
- Information
- Probability Theory, An Analytic View , pp. 304 - 333Publisher: Cambridge University PressPrint publication year: 2024