I have a presentation to give on Markov Renewal Theory and Semi Markov processes but I cannot really find enough "interesting" examples to talk about, apart from the usual finance-related ones. It seems to be all about equations and integrals and seems quite dull to me.
I am not sure if the book I am referring to, Cinlar, is good for this purpose. Markov chain has many interesting examples and topics to talk about, like card shuffling, random walks, etc. I am not sure if such interesting elements are there in semi markov processes, behind all those limit theorems and equations, it seems.