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arXiv · 0909.1307

A construction of the rough path above fractional Brownian motion using Volterra's representation

David Nualart·Samy Tindel
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Abstract

This note is devoted to construct a rough path above a multidimensional fractional Brownian motion $B$ with any Hurst parameter $H\in(0,1)$, by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to [Stochastic Process. Appl. 120 (2010) 1444--1472], where the construction of a rough path over $B$ was first introduced.

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David Nualart, Samy Tindel. 2009-09-07. A construction of the rough path above fractional Brownian motion using Volterra's representation. https://doi.org/10.1214/10-aop578

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