I am working though the book of J. Norris, "Markov Chains" as self-study and have difficulty with ex. 2.7.1, part a.
The exercise can be read through Google books. My understanding is that the probability is given by
(0,i) matrix element of
exp(t*Q). Setting up forward evolution equation leads to differential difference equation which I was hinted admits no closed form solution (see my question on mathoverflow).
I obviously need an nudge in a right direction, and the exercise must admit a simple solution. Any directions are much appreciated.