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

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.

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

References in corpus (2)

• Stochastic calculus for fractional Brownian motion with Hurst exponent $H>1/4$: A rough path method by analytic extension
• Relating two Hopf algebras built from an operad

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