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 t...

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Bibliographic Details
Main Authors: Yann Vestring, Javad Tavakoli
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/23/3641
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Summary: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.
ISSN:2227-7390