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Probability & Statistics/Proof of the detailed balance equations

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Question
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?

Answer
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:
http://www.netlab.tkk.fi/opetus/s383143/kalvot/E_bdpros.pdf

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Clyde Oliver

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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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I am a PhD educated mathematician working in research at a major university.

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Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

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BA mathematics & physics, PhD mathematics from a top 20 US school.

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Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

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In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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