I would like a more concrete understanding of what drift means for a stochastic process.
Is it possible for a stochastic process to have a non-zero drift term but zero expected value?
This doesn't make intuitive sense to me as my understanding of drift is that it measures the rate of change of the expected value of a stochastic process.
For example, the process $Z_t=tB_t$ has an expected value of 0 (where $B_t$ is a Brownian process). Using Ito's Lemma, $dZ_t$ can be found to be $dZ_t = B_tdt+tdB_t$. From my understanding, this would imply that a drift term $\mu=B_t$ exists, however, as previously found, the expected value is $Z_t$ is constant at 0.
What does the non-zero drift term in this example say about the expected value of the process and how can I interpret drift terms in general?