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Dimension for Martingales (1210.7381v3)
Published 27 Oct 2012 in math.PR and math.GT
Abstract: A martingale \int H.dZ is defined as having Dimension k if H has rank k almost surely, almost all t. Dimension can be used as a geometric invariant to classify and study martingales. We also define general Brownian motions in higher dimensions.
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