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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2024-11-01
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| author | Yann Vestring Javad Tavakoli |
| author_facet | Yann Vestring Javad Tavakoli |
| author_sort | Yann Vestring |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9ae9d3b35513451da825ec4a12499da8 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9ae9d3b35513451da825ec4a12499da82024-12-13T16:27:16ZengMDPI AGMathematics2227-73902024-11-011223364110.3390/math12233641Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov ChainYann Vestring0Javad Tavakoli1Department of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, CanadaDepartment of Mathematics, University of British Columbia Okanagan, 3187 University Way, Kelowna, BC V1V 1V7, CanadaDiscrete, 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.https://www.mdpi.com/2227-7390/12/23/3641Markov chainestimationsteady-state distributionconfidence intervalconfidence region |
| spellingShingle | Yann Vestring Javad Tavakoli Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain Mathematics Markov chain estimation steady-state distribution confidence interval confidence region |
| title | Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain |
| title_full | Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain |
| title_fullStr | Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain |
| title_full_unstemmed | Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain |
| title_short | Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain |
| title_sort | confidence regions for steady state probabilities and additive functionals based on a single sample path of an ergodic markov chain |
| topic | Markov chain estimation steady-state distribution confidence interval confidence region |
| url | https://www.mdpi.com/2227-7390/12/23/3641 |
| work_keys_str_mv | AT yannvestring confidenceregionsforsteadystateprobabilitiesandadditivefunctionalsbasedonasinglesamplepathofanergodicmarkovchain AT javadtavakoli confidenceregionsforsteadystateprobabilitiesandadditivefunctionalsbasedonasinglesamplepathofanergodicmarkovchain |