Posterior bounds on the equilibrium distribution of a finite markov chain

Abstract

Let P denote the transition probability matrix of a finite Markov chain with one recurrent class of states and consequently a unique equilibrium distribution . This paper exhibits bounds of the form for any allowed estimate x of ρ. These bounds are sharp when , and monotone inward under the usual iterative scheme . These bounds and monotonicity properties are a generalization of MacQueen's bounds on the fixed point of a monotone contraction operator