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

Author

Listed:
  • Yann Vestring

    (Department of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, Canada
    These authors contributed equally to this work.)

  • Javad Tavakoli

    (Department of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, Canada
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Yann Vestring & Javad Tavakoli, 2024. "Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain," Mathematics, MDPI, vol. 12(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3641-:d:1526024
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    References listed on IDEAS

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    1. Cruz, Juan Alberto Rojas, 2020. "Sensitivity of the stationary distributions of denumerable Markov chains," Statistics & Probability Letters, Elsevier, vol. 166(C).
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