Optimitation and perturbation analysis in the stationary distribution of a Markov Chain

We consider a stationary distribution of a finite, irreducible, homogeneous Markov chain. Our aim is to perturb the transition probabilities matrix using approximations to find regions of feasibility and optimality for a given basis when the chain is optimized using linear programming. We also explore the application of perturbations bonds and analyze the effects of these on the construction of optimal policies.