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!