Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!

2021/02/25 by T'Joens, Natan, De Bock, Jasper
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2102.13075

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.

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