Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!
Probability
2021-04-30 v2
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
@article{arxiv.2102.13075,
title = {Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!},
author = {Natan T'Joens and Jasper De Bock},
journal= {arXiv preprint arXiv:2102.13075},
year = {2021}
}