Some time back I was reading a PDF about algebra or topology (or algebraic topology, I forget which) and found an extremely enlightening section about an application to stochastic processes. Essentially they defined a stochastic processes $X_t$ and defined some function $y(T)$ to be the number of times between $t=0$ and $t=T$ that $X_t=c$, for some $c$. They used either algebra or topology to shed light on the structure of that problem. It was extremely interesting but I've forgotten where I saw it and was wondering if anyone had a hint of what I might have been looking at (in terms of the math or the doc itself). Perhaps I will be able to track it down again!
Any thoughts of applications of either algebra, topology or algebraic topology to stochastic processes, particular ones with the Markov property?