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

TL;DR

This paper presents a new method to construct rough paths over multidimensional fractional Brownian motion using Volterra's representation, simplifying algebraic and computational aspects compared to previous approaches.

Contribution

It introduces a novel construction of rough paths over fractional Brownian motion via Volterra representation, enhancing simplicity and efficiency.

Findings

Simplified algebraic structure for rough path construction

Reduced computational complexity in the construction process

Applicable to any Hurst parameter in (0,1)

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.