Markov chain

giglamesh

Hello all
I have a question about Markov chain I've obtained in an application.
There is no need to mention the application or the details of markov chain because my question is simply:

The transition probabilities are derived with equations that depend on the stationary probability, I know it's something complicated ...

The question is:
1. do you know what is the class of these markov chains?
2. how to solve it numerically, does it depend on Power method?

If you have any paper or book it will be great
Thanks