Suppose that $\phi(t,x):[0,\infty)\times \mathbb{R}^d\rightarrow \mathbb{R}^d$ is a flow. Is it possible to extend $\phi$ to a family of stochastic flows $\{\Phi(t,x,\sigma)\}_{\sigma \in [0,1]}$ such that
For every $\sigma_0 \in (0,1]$, $\Phi(t,x,\sigma_0):[0,\infty)\times \mathbb{R}^d\righta...