Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All the Same!
Abstract
We consider three different types of global uncertainty models for discrete-time stochastic processes: measure-theoretic upper expectations, game-theoretic upper expectations and axiomatic upper expectations. The last two are known to be identical. We show that they coincide with measure-theoretic upper expectations on two distinct domains: monotone pointwise limits of finitary gambles, and bounded below Borel-measurable variables. We argue that these domains cover most practical inferences, and that therefore, in practice, it does not matter which model is used.
Cite
Text
T’Joens and De Bock. "Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All the Same!." Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, 2021.Markdown
[T’Joens and De Bock. "Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All the Same!." Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, 2021.](https://mlanthology.org/isipta/2021/tjoens2021isipta-global/)BibTeX
@inproceedings{tjoens2021isipta-global,
title = {{Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All the Same!}},
author = {T’Joens, Natan and De Bock, Jasper},
booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications},
year = {2021},
pages = {310-319},
volume = {147},
url = {https://mlanthology.org/isipta/2021/tjoens2021isipta-global/}
}