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1 vote

An integral by rough path.

This is an old question but it's quite interesting. Here is an attempt with some extra assumptions because $f$ and $b$ are not concrete. The reasonable approach is to try to find a Gubinelli ...
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0 votes

Uniqueness of solutions of Young differential equations

For such small $\beta$, we need to use Rough path theory to make sense of the integral and so below I go over that. (Indeed for $\beta\in (\frac{1}{2},1]$, there is an ODE theory for Young integrals ...
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2 votes
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Let $X^n$ be a collection of smooth functions so that their $\alpha$-Holder norms are uniformly bounded

This cannot hold, and in a sense rough path theory has to be developed precisely because of this reason; otherwise, rough path lifts would be defined uniquely for any curve of Hölder regularity $>1/...
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