English

Dimension for Martingales

Probability 2012-11-06 v3 Geometric Topology

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.

Keywords

Cite

@article{arxiv.1210.7381,
  title  = {Dimension for Martingales},
  author = {Prabhu Janakiraman},
  journal= {arXiv preprint arXiv:1210.7381},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T22:28:45.282Z