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I have another problem from Koralov-Sinai that I don't know how to do and I would appreciate help please. It goes like this:

5.16. Consider a Markov chain whose state space is the unit circle. Let the density of the transition function $P(x,dy)$ be given by $p(x,y) = \frac{1}{2 \epsilon}$ if the angle $(y,x) < \epsilon$ and $0$ otherwise. Find the stationary distribution.

Thank you all!

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    The definite article is a giveaway -- if there's only one stationary distribution and the transition function exhibits rotational symmetry, what would you expect regarding the symmetry properties of the stationary distribution?2012-11-06
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    can you post a complete answer please? I'm struggling with the concepts...2012-11-06
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    I'm assuming you mean we get a reversible distribution... but I don't see how to prove it2012-11-06
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    I'm still lost with this; can anyone help?2012-11-07

1 Answers 1