Martingales with Independent Increments

Published 26 Jun 2024 in math.PR | (2406.18716v3)

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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Freddy Delbaen

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