The Brownian Frame Process as a Rough Path
Probability
2007-05-23 v1
Abstract
We introduce the (path-valued) Brownian frame process whose evaluation at time t is the sample path of the underlying Brownian motion run from time t-1 to t. Due to its connections with Gaussian Volterra processes and SDDEs this is an interesting object to study. The first part deals with path-wise properties of the Brownian frame process in the p-variation norm. The second part shows the non-existence of a Levy area random variable in a particular norm, revealing the difficulty in establishing a Rough Path integration theory for the Brownian Frame process.
Cite
@article{arxiv.math/0602008,
title = {The Brownian Frame Process as a Rough Path},
author = {Benjamin Hoff},
journal= {arXiv preprint arXiv:math/0602008},
year = {2007}
}