I'm working on a problem where I've run into a generalized ODE
$$ \dot X \in D(X) $$
where $D(X)$ is a continuous, compact and convex subset of $\mathbf{R}^n$. To me, this problem seems in many ways similar to problems involving stochastic differential equations (SDE). Just out of curiosity I wonder if there are any clear parallels or direct connections between the theory of generalized odes and SDEs. If not, I would also be interested in which key way they differ.
Note that an answer in layman terms would be most helpful since I'm not a really a mathematician.