I have a random walk process, discrete in time and state, where at each step the probability of $+1$ is $p$ and $−1$ is $q$. $p+q=1$ and $p$ may be different from $q$ (i.e. the random walk is "biased", "asymmetric", has "drift").
Starting from $x$, where $a<x<b$, I'd like to find the expected hitting time to hit either $a$ or $b$.
There's usually a nonzero probability of the random walk never hitting either boundary, which may imply difficulties getting an expectation. So a median of the hitting time distribution could be a useful alternative, if that can be expressed well.
My question seems related to other hitting time questions such as this on the time of first return and this on the distribution of the hitting time. However I'm rather unsure how to go to those helpful points to the expectation, and to the answer regarding hitting either boundary.