I have a stochastic process representing a non homogeneous Markov chain. The transition matrix between and is given by
From the time , the transition matrix between and becomes time independent and is given by
For homgeneous Markov chains, it is well know that
is the number of times the process visits the transient state before it eventually enters a recurrent state, having initially started from the transient state .
is the identity matrix.
is the transition matrix between transient states.
How can I obtain the number of visits for my case?
Can I transform the non homogeneous model to a homogeneous one?