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
2 - The Central Limit Theorem
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
Chapter 2 is devoted to the classical Central Limit Theorem. The initial presentation is based on Lindeberg’s non-Fourier techniques. This is followed by a derivation of the Berry–Esseen estimate based on ideas of C. Stein. Fourier techniques are introduced in §2.3, and in the final section the CLT is used to derive W. Beckner’s sharp Lpestimates for the Fourier transform.
- Type
- Chapter
- Information
- Probability Theory, An Analytic View , pp. 51 - 100Publisher: Cambridge University PressPrint publication year: 2024