Kolmogorov type and general extension results for nonlinear expectations
Abstract
We provide extension procedures for nonlinear expectations to the space of all bounded measurable functions. We first discuss a maximal extension for convex expectations which have a representation in terms of finitely additive measures. One of the main results of this paper is an extension procedure for convex expectations which are continuous from above and therefore admit a representation in terms of countably additive measures. This can be seen as a nonlinear version of the Daniell-Stone theorem. From this, we deduce a robust Kolmogorov extension theorem which is then used to extend nonlinear kernels to an infinite dimensional path space. We then apply this theorem to construct nonlinear Markov processes with a given family of nonlinear transition kernels.
Keywords
Cite
@article{arxiv.1511.08726,
title = {Kolmogorov type and general extension results for nonlinear expectations},
author = {Robert Denk and Michael Kupper and Max Nendel},
journal= {arXiv preprint arXiv:1511.08726},
year = {2018}
}