TITLE: Most likely path through a continuous time Markov chain
QUESTION [1 upvotes]: If I have a discrete Markov chain, it's easy to find the most likely path through it: just look at the probabilities of following each possible path independently, and take the largest one. 
In a continuous chain I am wondering if the same process works: that is, is the fastest path through a continuous time Markov chain just the most likely path through its respective embedded chain? Or, alternatively, could it be different? 
Thanks in advance for the help.

REPLY [2 votes]: If I understand you correctly, the question is "What is the most likely path (sequence of states) of a continuous-time Markov chain (CTMC), given some evolution time $t$ and possibly intitial and/or final state?"
This problem has been solved here through a "Viterbi-like" dynamic programming algorithm. Matlab and R implementations are available for download as well. While the paper talks about ion channels and HIV drug resistance, the results are applicable to any CTMC.
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