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
3 - Infinitely Divisible Laws
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
This chapter is devoted to the study of infinitely divisible laws. It begins in §3.1 with a few refinements (especially the Lévy Continuity Theorem) of the Fourier techniques introduced in §2.3. These play a role in §3.2, where the Lévy–Khinchine formula is first derived and then applied to the analysis of stable laws.
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- Probability Theory, An Analytic View , pp. 101 - 130Publisher: Cambridge University PressPrint publication year: 2024