The Brownian Frame Process as a Rough Path

Benjamin Hoff

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arXiv · math/0602008

The Brownian Frame Process as a Rough Path

Benjamin Hoff

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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.

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Benjamin Hoff. 2006-02-01. The Brownian Frame Process as a Rough Path. https://arxiv.org/abs/math/0602008

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