A CONSTRUCTION OF THE ROUGH PATH ABOVE FRACTIONALBROWNIAN MOTION USING VOLTERRA'S REPRESENTATION

摘要

This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H (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.