@SiongThyeGoh a quick question, how can we find stationary distrinbution of a reducible Markov Chain ?

i dont' think we can even guarantee the uniqueness right? might want to analyze some irreducible component and analyze?

Why cant guarantee uniqueness?@SiongThyeGoh what is the motivation about it?

there is a result that if it is irreducible, then it is unique right? if it is not reducible, consider a markov chain with two irreducible components, then each component has their own stationary distribution (setting the other component that corresponds to the other component to be 0). Hence we have construted two stationary distribution right? also any convex combination of them is another stationary distribution.

extreme example is the identity matrix where each nonnegative vector that sums to 1 is a valid stationary distribution.