Martingales with Independent Increments
Probability
2024-12-09 v3
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 martingale is the sum of a series of Gaussian martingales.
Keywords
Cite
@article{arxiv.2406.18716,
title = {Martingales with Independent Increments},
author = {Freddy Delbaen},
journal= {arXiv preprint arXiv:2406.18716},
year = {2024}
}