Hitting Times and Probabilities for Imprecise Markov Chains

Thomas Krak, Natan T’Joens, Jasper De Bock
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:265-275, 2019.

Abstract

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-krak19a, title = {Hitting Times and Probabilities for Imprecise Markov Chains}, author = {Krak, Thomas and T'Joens, Natan and De Bock, Jasper}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {265--275}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/krak19a/krak19a.pdf}, url = {https://proceedings.mlr.press/v103/krak19a.html}, abstract = {We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains.} }
Endnote
%0 Conference Paper %T Hitting Times and Probabilities for Imprecise Markov Chains %A Thomas Krak %A Natan T’Joens %A Jasper De Bock %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-krak19a %I PMLR %P 265--275 %U https://proceedings.mlr.press/v103/krak19a.html %V 103 %X We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains.
APA
Krak, T., T’Joens, N. & De Bock, J.. (2019). Hitting Times and Probabilities for Imprecise Markov Chains. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:265-275 Available from https://proceedings.mlr.press/v103/krak19a.html.

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