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# 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*, 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.