Take a look at Friz and Shekhar General rough integration, Levy rough paths and a Levy-Kintchine type formula.
Regarding the Holder condition, don't Brownian motions themselves qualify?
Take a look at Friz and Shekhar General rough integration, Levy rough paths and a Levy-Kintchine type formula.
Regarding the Holder condition, don't Brownian motions themselves qualify?