Martingales with Independent Increments

Freddy Delbaen

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arXiv · 2406.18716

Martingales with Independent Increments

Freddy Delbaen

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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 $L^2$ martingale is the sum of a series of Gaussian martingales.

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BibTeX RIS

Freddy Delbaen. 2024-06-26. Martingales with Independent Increments. https://arxiv.org/abs/2406.18716

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