Hitting times for continuous-time imprecise-Markov chains

Thomas Krak
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1031-1040, 2022.

Abstract

We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work essentially constitute sets of stochastic processes. Their inferences are tight lower- and upper bounds with respect to variation within these sets. We consider three distinct types of these models, corresponding to different levels of generality and structural independence assumptions on the constituent processes. Our main results are twofold; first, we demonstrate that the hitting times for all three types are equivalent. Moreover, we show that these inferences are described by a straightforward generalization of a well-known linear system of equations that characterizes expected hitting times for traditional time-homogeneous continuous-time Markov chains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-krak22a, title = {Hitting times for continuous-time imprecise-{M}arkov chains}, author = {Krak, Thomas}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1031--1040}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/krak22a/krak22a.pdf}, url = {https://proceedings.mlr.press/v180/krak22a.html}, abstract = {We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work essentially constitute sets of stochastic processes. Their inferences are tight lower- and upper bounds with respect to variation within these sets. We consider three distinct types of these models, corresponding to different levels of generality and structural independence assumptions on the constituent processes. Our main results are twofold; first, we demonstrate that the hitting times for all three types are equivalent. Moreover, we show that these inferences are described by a straightforward generalization of a well-known linear system of equations that characterizes expected hitting times for traditional time-homogeneous continuous-time Markov chains.} }
Endnote
%0 Conference Paper %T Hitting times for continuous-time imprecise-Markov chains %A Thomas Krak %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-krak22a %I PMLR %P 1031--1040 %U https://proceedings.mlr.press/v180/krak22a.html %V 180 %X We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work essentially constitute sets of stochastic processes. Their inferences are tight lower- and upper bounds with respect to variation within these sets. We consider three distinct types of these models, corresponding to different levels of generality and structural independence assumptions on the constituent processes. Our main results are twofold; first, we demonstrate that the hitting times for all three types are equivalent. Moreover, we show that these inferences are described by a straightforward generalization of a well-known linear system of equations that characterizes expected hitting times for traditional time-homogeneous continuous-time Markov chains.
APA
Krak, T.. (2022). Hitting times for continuous-time imprecise-Markov chains. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1031-1040 Available from https://proceedings.mlr.press/v180/krak22a.html.

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