Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
| Autor: | Natan T'Joens, Jasper De Bock |
|---|---|
| Přispěvatelé: | Lesot, Marie-Jeanne |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
media_common.quotation_subject
02 engineering and technology Type (model theory) Upper and lower bounds Article Weak Ergodicity 020204 information systems 0202 electrical engineering electronic engineering information engineering Imprecise Markov chain FOS: Mathematics Limit (mathematics) Statistical physics Weak ergodicity Mathematics media_common Upper expectation Markov chain Probability (math.PR) State (functional analysis) Infinity Expected time average Mathematics and Statistics Discrete time and continuous time 020201 artificial intelligence & image processing Upper transition operator Mathematics - Probability |
| Zdroj: | Information processing and management of uncertainty in knowledge-based systems, 18th International Conference, IPMU 2020, Lisbon, Portugal, June 15-19, 2020, Proceedings, Part II Information Processing and Management of Uncertainty in Knowledge-Based Systems ISBN: 9783030501426 IPMU (2) Information Processing and Management of Uncertainty in Knowledge-Based Systems |
| ISSN: | 1865-0929 1865-0937 |
| Popis: | 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 set of necessary and sufficient conditions 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 conditions are 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. |
| Databáze: | OpenAIRE |
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