Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain

Discrete, finite-state Markov chains are applied in many different fields. When a system is modeled as a discrete, finite-state Markov chain, the asymptotic properties of the system, such as the steady-state distribution, are often estimated based on a single, empirically observable sample path of the system, whereas the actual steady-state distribution is unknown. A question that arises is: how close is the empirically estimated steady-state distribution to the actual steady-state distribution? In this paper, we propose a method to numerically determine asymptotically exact confidence regions for the steady-state probabilities and confidence intervals for additive functionals of an ergodic Markov chain based on a single sample path.