I am looking for methods to approximate the stationary distribution of an infinite CTMC with a sparse rate matrix. Each row and column of the rate matrix has a finite number of non-zero elements. There is this paper Bounding the equilibrium distribution of Markov population models by Dayar et al. that identifies a region of the state space where most of the probability of the stationary distribution is concentrated and then finds upper and lower bounds on the stationary probabilities for the states in that region.

I wondered whether there was something similar for other classes of CTMC or something a bit more general.

A lot of what I've found has been applicable to various classes of queue systems but my case doesn't fall within that.