Rough path limits of the Wong–Zakai type with a modified drift term

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Integrability Estimates for Gaussian Rough Differential Equations (2011, background): “Worse still, the work Oberhauser and Friz [7] shows that the inequality (1.2) can actually be saturated for a (deterministic) choice of diﬀerential equation and driving rough path.”
Canonical RDEs and general semimartingales as rough paths (2017, background): “, in homogenization theory [34, 15, 28] and non-standard approximations to Brownian motion [41, 16].”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, methodology): “It is therefore interesting to know that this estimate cannot be improved and the reader can find a construction of the relevant examples in [54].”
Flows driven by rough paths (2012, background): “(3) The above theorem provides a straightforward justification of Friz and Oberhauser’s theorem about drift induced by perturbed driving signals; theorem 2 in [15].”
Discretely sampled signals and the rough Hoff process (2013, result): “20] and [4] for similar results concerning lead-lag driven random ODE convergence.”