Dimension for Martingales
arXiv:1210.7381
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.
16 pg. Main changes from v2: Section 4 revised, definition of R^{nxm}_K Brownian motion modified; some changes in general discussions, sec 6.2