I have heard the phrase a lot when someone refers to a stochastic process as being "driven by a Brownian motion" or the "levy process that drives it" etc.
In this context, what is meant by "driving process"?
I assume it means something like if a process $X(t)$ can be defined using the SDE
$$dX_t = a(t,X_t) dt + B(t) dW_t$$
Then it is driven by the process $W_t$? But I'm not sure of the exact definition.