Augmented truncation approximations of discrete-time Markov chains

Abstract

Let P be a positive recurrent infinite transition matrix with invariant distribution π and ( n ) P ̃ be a truncated and arbitrarily augmented stochastic matrix with invariant distribution ( n ) π . We investigate the convergence ‖ ( n ) π − π ‖ → 0 , as n → ∞ , and derive a widely applicable sufficient criterion. Moreover, computable bounds on the error ‖ ( n ) π − π ‖ are obtained for polynomially and geometrically ergodic chains. The bounds become rather explicit when the chains are stochastically monotone.