Regarding Theorem 3.1 of "A Course on Rough Paths" by Friz and Hairer below:
The proof states that one may assume WLOG that $T = 1$. Is this due to scaling, i.e., we prove the case for $[0,1]$, then the theorem holds for the scaled process $[0,1] \ni t \mapsto X(t\cdot T)$, which is equivalent to the process $[0,T] \ni t \mapsto X(t)$?
2026-02-23 08:43:06.1771836186
Correct scaling argument in proof of Kolmogorov criterion for rough paths?
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