What's the difference between a state-transition-matrix and a transition matrix (say, for an ergodic Markov Chain) that is typically taught in a basic probability theory course? This is the first time I have heard of a state-transition-matrix.
Wikipedia does not offer much reading material on it.
I found some online notes from a university but, weirdly, what I am reading is a bunch of differential equations.
Are the entries of the state-transition-matrix analogous to the transition probabilities of a transition matrix (of some Markov chain)?
Thanks,