I hope the question is not too vague. My calculus courses are way in the past and I can't remember how to do it :-).
I have this master equation for a time-continuous Markov chain
I have a two state system $(A, B)$ and the transition rates $q_{BA}$ and $q_{AB}$. And now I want probability of the system being in state $A$ after an amount of time $t$. Do I have to take the values at $t_{0}$ for $P_{A}(t)$ and $P_{B}(t)$? I'm quite at a loss...