= Stroock-Varadhan support theorem
{c}
{title2=$\operatorname{supp}\mathcal L(Y)=\overline{\{y^h:h\in H_0^1\}}$}
For smooth bounded vector fields, the support of a Stratonovich diffusion in uniform path topology is the closure of solutions to the controlled <ordinary differential equation> with the same drift and controls in the <Cameron-Martin space of Wiener measure>. The <support of enhanced Brownian motion> and the <universal limit theorem> prove this through continuity of the enhanced solution map. For an equation written in Itô form, the controlled drift is the Itô drift minus $\tfrac12\sum_iDV_iV_i$.
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