User:TheLarry/Notebook/Larrys Notebook/2009/09/18

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Continuous Time Markov Chains

After finishing that chapter yesterday, and working through the examples I feel like I have a decent grasp on Markov chains. The major problem I am coming into is that there is an assumption that there is a uniform time between states (or in states depending how you look at it). Because of this I am trying to find some one who uses Markov chains with changing times. I think this might be called Continuous Time Markov Chains. I am not sure yet because there are a slew of different types of Markov Chains. But this looks promising I am going to try to find a resource so i can learn what this is all about.

Steve Koch 21:51, 18 September 2009 (EDT): I'm still not understanding you completely. But wondering if maybe what you're saying is that you learned a lot about general markov chains, and now want to learn about our specific case? I think poisson process will help you a lot.
TheLarry 23:07, 18 September 2009 (EDT): All I am saying is that everything i have read so far doesn't keep track of time it takes to take each step. It just keeps track of how many steps were taken. But I am guessing that it is possible to keep track of the time as well. Some one must have done it. But I'll look at the Poisson.
I just looked up the Poisson, and it looks intriguing, but it shouldn't be this hard. I just wanna say that this transition takes this long. So let's keep track of the total time. So I can just say this transition happened so i add the time on. So I can find out the average time it takes. Now I think i can basically do it with the knowledge I have but there has to be a better way out there since this seems like a common problem.