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

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

2009-09-07

arxiv.org/abs/0909.1307v2

Annals of Probability (2011) Vol. 39, no. 3, 1061-1096

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP578 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP578

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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