  We give a causal interpretation of stochastic differential equations (SDEs)
by defining the postintervention SDE resulting from an intervention in an SDE.
We show that under Lipschitz conditions, the solution to the postintervention
SDE is equal to a uniform limit in probability of postintervention structural
equation models based on the Euler scheme of the original SDE, thus relating
our definition to mainstream causal concepts. We prove that when the driving
noise in the SDE is a L\'evy process, the postintervention distribution is
identifiable from the generator of the SDE.
