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Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain Vestring, Yann; Tavakoli, Javad

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.

Item Metadata

Title
Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain
Creator
Vestring, Yann; Tavakoli, Javad
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2024-11-21
Description
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.
Subject
Markov chain; estimation; steady-state distribution; confidence interval; confidence region
Genre
Article
Type
Text
Language
eng
Date Available
2024-12-18
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0447553
URI
http://hdl.handle.net/2429/89930
Affiliation
Science, Irving K. Barber Faculty of (Okanagan); Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Citation
Mathematics 12 (23): 3641 (2024)
Publisher DOI
10.3390/math12233641
Peer Review Status
Reviewed
Scholarly Level
Faculty
Rights URI
https://creativecommons.org/licenses/by/4.0/
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CC BY 4.0