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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?

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  • $\begingroup$ I suggest you write to support@wolfram.com and ask. They will probably give you all the details you need (e.g. the paper reference). $\endgroup$ – Szabolcs May 2 '13 at 21:15
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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.

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