# Applications of algebra and/or topology to stochastic (or Markov) processes

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!

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I can't think of any application at this moment, but I certainly would be very interested in reading that PDF, if you find it once again! –  Jose L. Lykón Sep 22 '11 at 23:07
It's so annoying, goddam Windows crashed and I had to reboot so I lost all my open tabs in Chrome. Now I can't find the single best piece of math I've ever seen. It even had a discussion about how the reason most people haven't heard of the application is because most mathematicians aren't interested in both statistics and topology. Fascinating. –  Jason Sep 23 '11 at 13:51
@Jason You do know that chrome keeps a history of pages visited, right? It should be in there. I think you can even do a keyword search on the name of the page. –  Faheem Mitha Jan 30 '13 at 16:16