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Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our...

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Detalles Bibliográficos
Autores principales: T’Joens, Natan, De Bock, Jasper
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274679/
http://dx.doi.org/10.1007/978-3-030-50143-3_17
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author T’Joens, Natan
De Bock, Jasper
author_facet T’Joens, Natan
De Bock, Jasper
author_sort T’Joens, Natan
collection PubMed
description We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our main result is a necessary and sufficient condition under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process’ initial state. Remarkably, our condition is considerably weaker than those needed to establish similar results for so-called limit—or steady state—upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages.
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spelling pubmed-72746792020-06-08 Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains T’Joens, Natan De Bock, Jasper Information Processing and Management of Uncertainty in Knowledge-Based Systems Article We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our main result is a necessary and sufficient condition under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process’ initial state. Remarkably, our condition is considerably weaker than those needed to establish similar results for so-called limit—or steady state—upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages. 2020-05-15 /pmc/articles/PMC7274679/ http://dx.doi.org/10.1007/978-3-030-50143-3_17 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
T’Joens, Natan
De Bock, Jasper
Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title_full Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title_fullStr Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title_full_unstemmed Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title_short Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
title_sort limit behaviour of upper and lower expected time averages in discrete-time imprecise markov chains
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274679/
http://dx.doi.org/10.1007/978-3-030-50143-3_17
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