Average Behaviour of Imprecise Markov Chains: A Single Pointwise Ergodic Theorem for Six Different Models

Jasper De Bock, Natan T’Joens
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:90-99, 2021.

Abstract

We study the average behaviour of imprecise Markov chains; a generalised type of Markov chain where local probabilities are partially specified, and where structural assumptions such as Markovianity are weakened. In particular, we prove a pointwise ergodic theorem that provides (strictly) almost sure bounds on the long term average of any real function of the state of such an imprecise Markov chain. Compared to an earlier ergodic theorem by De Cooman et al. (2006), our result requires weaker conditions, provides tighter bounds, and applies to six different types of models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-de-bock21a, title = {Average Behaviour of Imprecise Markov Chains: A Single Pointwise Ergodic Theorem for Six Different Models}, author = {De Bock, Jasper and T'Joens, Natan}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {90--99}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/de-bock21a/de-bock21a.pdf}, url = {https://proceedings.mlr.press/v147/de-bock21a.html}, abstract = {We study the average behaviour of imprecise Markov chains; a generalised type of Markov chain where local probabilities are partially specified, and where structural assumptions such as Markovianity are weakened. In particular, we prove a pointwise ergodic theorem that provides (strictly) almost sure bounds on the long term average of any real function of the state of such an imprecise Markov chain. Compared to an earlier ergodic theorem by De Cooman et al. (2006), our result requires weaker conditions, provides tighter bounds, and applies to six different types of models.} }
Endnote
%0 Conference Paper %T Average Behaviour of Imprecise Markov Chains: A Single Pointwise Ergodic Theorem for Six Different Models %A Jasper De Bock %A Natan T’Joens %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-de-bock21a %I PMLR %P 90--99 %U https://proceedings.mlr.press/v147/de-bock21a.html %V 147 %X We study the average behaviour of imprecise Markov chains; a generalised type of Markov chain where local probabilities are partially specified, and where structural assumptions such as Markovianity are weakened. In particular, we prove a pointwise ergodic theorem that provides (strictly) almost sure bounds on the long term average of any real function of the state of such an imprecise Markov chain. Compared to an earlier ergodic theorem by De Cooman et al. (2006), our result requires weaker conditions, provides tighter bounds, and applies to six different types of models.
APA
De Bock, J. & T’Joens, N.. (2021). Average Behaviour of Imprecise Markov Chains: A Single Pointwise Ergodic Theorem for Six Different Models. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:90-99 Available from https://proceedings.mlr.press/v147/de-bock21a.html.

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