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

David Nualart (1) , Samy Tindel (2)

1 Department of Mathematics [Lawrence, Kansas]
2 BIGS - Biology, genetics and statistics

This note is devoted to construct a rough path above a multidimensional fractional Brownian motion $B$ with any Hurst parameter H lesser than 1/2, by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to a recent preprint by Unterberger, where the construction of a rough path over $B$ was first introduced.

Mots clés: Fractional Brownian motion; Multiple stochastic integrals; Rough paths theory

Domaines: Probabilités [math.PR]

David Nualart, Samy Tindel. A construction of the rough path above fractional Brownian motion using Volterra's representation. Annals of Probability, 2011, 39 (3), pp.1061-1096. ⟨10.1214/10-AOP578⟩. ⟨hal-00414075⟩