Given rates α of an irreducible continuous-time MC on finite state space and told that π is the invariant probability measure of this chain, we define a discrete time MC as having transition probabilities p(x,y) = α(x,y)/α(y).
I need to find the invariant probability of this discrete time chain in terms of π and α.
I'm not quite sure where to start. I tried just drawing out the NxN matrix and computing the invariant probability by hand, but I'm hoping for a better way to do this.