What algorithm is Mathematica 9 using for
FirstPassageTimeDistribution? Is it attempting to use
PseudoInverse on the Laplacian of the graph underlying the discrete Markov process?
According to Wolfram Support:
First passage time distribution is defined by its characteristic function which is computed from the underlying Markov chain. The implementation has been based on a variety of references, but mostly based on the book by W.J. Steward, "Probability, Markov Chains, Queues and Simulation" which was found to be very comprehensive.