Transitional Probabilities and Repetitive Loops

[pfeaster]

Please forgive my ignorance. I taught myself everything I know about Markov chains from Wikipedia, in order to follow some of the good discussions that are happening these days about the statistical properties of the VMs text. My understanding of a Markov model of a dynamic system is one where the probability of any given state depends only on the state immediately prior. By "second-order transitional probability", I understand this to mean the probability of a state transition happening, given the prior two states, in the order they occurred. Do I understand this correctly?

That's what I meant by "second order" -- for example, the probability that [l] will occur after [do] rather than just [o].  But I'm admittedly a neophyte myself when it comes to Markov processes and the terminology behind them.

A related question I'm wondering about: how many states properly comprise a complete repetition? 

My sense is that there may be no fixed cycle length, much as there's no fixed vord length in "word grammars."  Otherwise I'd be tempted to speculate about something like a Vigenère key with one row assigned to nulls.  It seems as though a loop cycle can be longer or shorter depending on how many steps it takes to get back to an equivalent point again.  Some seemingly interchangeable paths appear shorter than others, e.g., [qok] versus [ch].  Of course I don't know why or what it means, if there's anything to it in the first place.