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
Published inMathematics (Basel) Vol. 12; no. 23; p. 3641
Main Authors Vestring, Yann, Tavakoli, Javad
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2024
Subjects
Analysis
Asymptotic properties
confidence interval
confidence region
estimation
Markov analysis
Markov chain
Markov chains
Markov processes
Steady state
steady-state distribution
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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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12233641