Publikation: Kolmogorov-type and general extension results for nonlinear expectations
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2018
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Banach Journal of Mathematical Analysis. 2018, 12(3), pp. 515-540. eISSN 1735-8787. Available under: doi: 10.1215/17358787-2017-0024
Zusammenfassung
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 article 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.
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510 Mathematik
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DENK, Robert, Michael KUPPER, Max NENDEL, 2018. Kolmogorov-type and general extension results for nonlinear expectations. In: Banach Journal of Mathematical Analysis. 2018, 12(3), pp. 515-540. eISSN 1735-8787. Available under: doi: 10.1215/17358787-2017-0024BibTex
@article{Denk2018Kolmo-32428.3,
year={2018},
doi={10.1215/17358787-2017-0024},
title={Kolmogorov-type and general extension results for nonlinear expectations},
url={https://projecteuclid.org/euclid.bjma/1510909221},
number={3},
volume={12},
journal={Banach Journal of Mathematical Analysis},
pages={515--540},
author={Denk, Robert and Kupper, Michael and Nendel, Max}
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2018-08-07
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