Is it possible that a system converge partially in a discrete markov desicion process? With "partially" I mean that some states has a value function convergent (steady state) but other states has a value function oscillating between some other values. I think that it is possible because if the transition matrix do not combine the convergent states with the oscillating states, there can be a fixed point.
I am studying from the book "Markov Desicion Processes" from Putterman (2014) but I can not find some section that answer me this question. Thanks, any help or literature will be grateful.