= Universal limit theorem
For sufficiently regular vector fields, for example bounded fields with bounded derivatives through order three when $2<p<3$, the solution map of a <rough differential equation> exists uniquely and is locally continuous in the <rough path metric>. <Ordinary differential equations> driven by smooth approximations therefore converge whenever their enhanced drivers converge. The theorem makes the enhancement, rather than just the original path, the correct input for a continuous solution map.
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