@article{EJP37,
author = {Stephen Montgomery-Smith},
title = {Concrete Representation of Martingales},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {3},
year = {1998},
keywords = {martingale, concrete representation, tangent sequence, condition (C.I.), UMD, Skorohod representation},
abstract = {Let $(f_n)$ be a mean zero vector valued martingale sequence. Then there exist vector valued functions $(d_n)$ from $[0,1]^n$ such that $\int_0^1 d_n(x_1,\dots,x_n)\,dx_n = 0$ for almost all $x_1,\dots,x_{n-1}$, and such that the law of $(f_n)$ is the same as the law of $(\sum_{k=1}^n d_k(x_1,\dots,x_k))$. Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker version of a result of McConnell that provides a Skorohod like representation for vector valued martingales.},
pages = {no. 15, 1-15},
issn = {1083-6489},
doi = {10.1214/EJP.v3-37},
url = {http://ejp.ejpecp.org/article/view/37}}