  We study a stochastically-driven standard map. The addition of a noise term
destroys the invariant manifolds that organize the phase space which allows for
more widespread transport than in the noiseless case. Using appropriately
defined hitting times to quantify the dynamics, we identify two qualitatively
different classes of transport: linear and nonlinear. Linear transport is
primarily driven by the stochasticity in the system, while nonlinear transport
results from a combination of the nonlinear dynamics and stochasticity and
provides a significant speed-up in transport.
