confusion with notes

[halasadi]

In the posterior computation section (pg 6),

one sentence says "If $q$ is chosen to be irreducible and aperiodic, then this Markov chain has stationary distribution".

I am a little confused here, are we talking about the markov chain with transition probabilities $q(x'|x)$ or the markov chain defined by q(x'|x) * A(x'|x)?