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Probability & Statistics/Proof of the detailed balance equations


Need help with Lemma 8.5
Need help with Lemma 8  

Close up of lemma 8.5
Close up of lemma 8.5  
Hello Clyde

I'm taking a course in stochastic processes and one of the Lemma's stated (Lemma 8.5) in my coursebook doesn't go through how it was derived.
I dont have any experience with proofs and it doesn't get taught in any of my courses, how did they reach this conclusion?

It is very easy to prove the contrapositive: If it is not true that the equations are balanced (8.0.1) for any i, then there is no stable state -- the net flow in node i will always be nonzero. You could state that more rigorously, but that's the gist of it.

The notes found here may also be of interest:

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.


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