  In this note we consider a family of nonlinear (conditional) expectations
that can be understood as a multidimensional diffusion with uncertain drift and
certain volatility. Here, the drift is prescribed by a set-valued function that
depends on time and path in a Markovian way. We establish the Feller property
for the associated sublinear Markovian semigroup and we observe a smoothing
effect as our framework carries enough randomness. Furthermore, we link the
corresponding value function to a semilinear Kolmogorov equation.
