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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.

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MLA
Krak, Thomas, et al. “Hitting Times and Probabilities for Imprecise Markov Chains.” International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock et al., vol. 103, PMLR, 2019, pp. 265–75.
APA
Krak, T., T’Joens, N., & De Bock, J. (2019). Hitting times and probabilities for imprecise Markov chains. In J. De Bock, C. de Campos, G. De Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings (Vol. 103, pp. 265–275). Ghent, Belgium: PMLR.
Chicago author-date
Krak, Thomas, Natan T’Joens, and Jasper De Bock. 2019. “Hitting Times and Probabilities for Imprecise Markov Chains.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock, Cassio de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:265–75. Ghent, Belgium: PMLR.
Chicago author-date (all authors)
Krak, Thomas, Natan T’Joens, and Jasper De Bock. 2019. “Hitting Times and Probabilities for Imprecise Markov Chains.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, ed by. Jasper De Bock, Cassio de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:265–275. Ghent, Belgium: PMLR.
Vancouver
1.
Krak T, T’Joens N, De Bock J. Hitting times and probabilities for imprecise Markov chains. In: De Bock J, de Campos C, De Cooman G, Quaeghebeur E, Wheeler G, editors. International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings. Ghent, Belgium: PMLR; 2019. p. 265–75.
IEEE
[1]
T. Krak, N. T’Joens, and J. De Bock, “Hitting times and probabilities for imprecise Markov chains,” in International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, Ghent, Belgium, 2019, vol. 103, pp. 265–275.
@inproceedings{8627473,
  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.},
  author       = {Krak, Thomas and T'Joens, Natan and De Bock, Jasper},
  booktitle    = {International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings},
  editor       = {De Bock, Jasper and de Campos, Cassio and De Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory},
  issn         = {2640-3498},
  language     = {eng},
  location     = {Ghent, Belgium},
  pages        = {265--275},
  publisher    = {PMLR},
  title        = {Hitting times and probabilities for imprecise Markov chains},
  url          = {http://proceedings.mlr.press/v103/},
  volume       = {103},
  year         = {2019},
}