Martingales with Independent Increments
Abstract
We show that a discrete time martingale with respect to a filtration with atomless innovations is the (infinite) sum of martingales with independent increments. For the continuous time filtration coming from Brownian Motion filtration, we show that every finite dimensional $L^2$ martingale is the sum of a series of Gaussian martingales.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Bulletin of the Belgian Mathematical Society - Simon Stevin
- Volume
- 33
- Issue
- 3
- Publication date
- 20 July 2026
- Language
- EN