Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces
Probability
2011-10-27 v2 Optimization and Control
Abstract
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our sublinear expectation, we give a simple construction, in a quasi-sure sense, of the (linear) conditional expectations, and hence give a representation for the conditional sublinear expectation. We also show an aggregation property holds, and give an equivalence between consistency and a pasting property of measures.
Keywords
Cite
@article{arxiv.1110.2592,
title = {Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces},
author = {Samuel N. Cohen},
journal= {arXiv preprint arXiv:1110.2592},
year = {2011}
}