I've been flipping through some literature on deriving the instantaneous state probabilities of a semi Markov stochastic process. However, I haven't been able to lay hands on a worked example involving non-exponential transitions. Could you please help with links to relevant references, published or unpublished? Thanks!
Also you may find an example in page 10 of
A large class of semi Markov processes can be written as the strong solution of a stochastic integral equation. That helps in many applications. See one such .
A basic reference is RA Howard (1971) Dynamic probabilistic systems Vol II.J Wiley
I would suggest the following book chapter by Professor Trivedi,
Trivedi, K., & Bobbio, A. (2017). Semi-Markov and Markov Regenerative Models. In Reliability and Availability Engineering: Modelling, Analysis, and Applications (pp. 509-550). Cambridge: Cambridge University Press. https://doi.org/10.1017/9781316163047.019
You can also learn other types of Markov Models such Phase Type and Regenerative Models.
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