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Re: Distribution of state occupancies in a multistate Markov model

• To: mathgroup at smc.vnet.net
• Subject: [mg104390] Re: Distribution of state occupancies in a multistate Markov model
• From: fd <fdimer at gmail.com>
• Date: Fri, 30 Oct 2009 02:17:52 -0500 (EST)
• References: <hc92bk$edu$1@smc.vnet.net>

Seth.

Well, I'm not sure if my approach is the one that suits what you need,
but let me try.

I would start looking if the chapman-kolmogorov equation can be
analytically solved

P(x1,t1|x0,t0)=Integrate P(x1,t1|x2,t2)P(x2,t2|x0,t0) dx2

integrate over all possible states x2. Depending on your transition
matrix, which are the P(x1,t1|x2,t2)'s, you may be able to perform
this integration..

please, take a look in Gardiner's book I mention below..on mackay's
book there are a few comments on chap 30..

refs:

David J. C. MacKay, Information Theory, Inference and learning
algorithms, Cambridge

You can find a copy of this book on-line if you agree not to print
it..

another good reference is the book by the new zealander physicist, C.
W. Gardiner, Handbook of Stochastic methods

good luck