Extending the Domain of Imprecise Jump Processes from Simple Variables to Measurable Ones

Alexander Erreygers, Jasper De Bock
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:140-149, 2021.

Abstract

We extend the domain of imprecise jump processes, also known as imprecise continuous-time Markov chains, from inferences that depend on a finite number of time points to inferences that can depend on the state of the system at all time points. We also investigate the continuity properties of the resulting lower and upper expectations with respect to point-wise convergent sequences that are monotone or dominated. For two particular inferences, integrals over time and the number of jumps to a subset of states, we strengthen these continuity properties and present an iterative scheme to approximate their lower and upper expectations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-erreygers21a, title = {Extending the Domain of Imprecise Jump Processes from Simple Variables to Measurable Ones}, author = {Erreygers, Alexander and De Bock, Jasper}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {140--149}, 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/erreygers21a/erreygers21a.pdf}, url = {https://proceedings.mlr.press/v147/erreygers21a.html}, abstract = {We extend the domain of imprecise jump processes, also known as imprecise continuous-time Markov chains, from inferences that depend on a finite number of time points to inferences that can depend on the state of the system at all time points. We also investigate the continuity properties of the resulting lower and upper expectations with respect to point-wise convergent sequences that are monotone or dominated. For two particular inferences, integrals over time and the number of jumps to a subset of states, we strengthen these continuity properties and present an iterative scheme to approximate their lower and upper expectations.} }
Endnote
%0 Conference Paper %T Extending the Domain of Imprecise Jump Processes from Simple Variables to Measurable Ones %A Alexander Erreygers %A Jasper De Bock %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-erreygers21a %I PMLR %P 140--149 %U https://proceedings.mlr.press/v147/erreygers21a.html %V 147 %X We extend the domain of imprecise jump processes, also known as imprecise continuous-time Markov chains, from inferences that depend on a finite number of time points to inferences that can depend on the state of the system at all time points. We also investigate the continuity properties of the resulting lower and upper expectations with respect to point-wise convergent sequences that are monotone or dominated. For two particular inferences, integrals over time and the number of jumps to a subset of states, we strengthen these continuity properties and present an iterative scheme to approximate their lower and upper expectations.
APA
Erreygers, A. & De Bock, J.. (2021). Extending the Domain of Imprecise Jump Processes from Simple Variables to Measurable Ones. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:140-149 Available from https://proceedings.mlr.press/v147/erreygers21a.html.

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