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?
TIA!
Best Answer
This looks like things Robert Adler is interested in, whether he calls it Stochastic Algebraic Topology or Random Fields. The links might help you get started.