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

Yann Vestring () and Javad Tavakoli
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Yann Vestring: Department of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, Canada
Javad Tavakoli: Department of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, Canada

Mathematics, 2024, vol. 12, issue 23, 1-11

Abstract: 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.

Keywords: Markov chain; estimation; steady-state distribution; confidence interval; confidence region (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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