An explicit rough path construction for continuous paths with arbitrary Hölder exponent, by Jeremie Unterberger (2009) [published with a different title]:

We construct an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in (0, 1)$. The method generalizes to arbitrary $\alpha$-Hölder paths the previous constructions that were limited to fractional Brownian motion. Our generalization may be coined as Fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies.

For a broader overview of this topic, starting from T. Lyon's seminal contributions, see Unterberger's Rough path theory.

An explicit rough path construction for continuous paths with arbitrary Hölder exponent, by Jeremie Unterberger (2009) [published with a different title]:

We construct an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in (0, 1)$. The method generalizes to arbitrary $\alpha$-Hölder paths the previous constructions that were limited to fractional Brownian motion. Our generalization may be coined as Fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. The method is not limited to Brownian motion, because it does not rely on tools belonging exclusively to the Gaussian realm, namely, the equivalence of $L^p$-norms due to the hypercontractivity property of the Ornstein-Uhlenbeck process.

For a broader overview of this topic with many examples, starting from T. Lyon's seminal contributions, see Unterberger's Rough Path Theory.

An explicit rough path construction for continuous paths with arbitrary Hölder exponent, J. Unterberger (2009) [published with a different title]:

We construct an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in (0, 1)$. The method generalizes to arbitrary $\alpha$-Hölder paths previously known constructions for multi-dimensional fractional Brownian motion. It may be coined as Fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies.

An explicit rough path construction for continuous paths with arbitrary Hölder exponent, by Jeremie Unterberger (2009) [published with a different title]:

We construct an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in (0, 1)$. The method generalizes to arbitrary $\alpha$-Hölder paths the previous constructions that were limited to fractional Brownian motion. Our generalization may be coined as Fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies.

For a broader overview of this topic, starting from T. Lyon's seminal contributions, see Unterberger's Rough path theory.