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Type of Publication: | Journal article |
Publication status: | Published |
Author: | Denk, Robert; Kupper, Michael; Nendel, Max |
Year of publication: | 2018 |
Published in: | Banach Journal of Mathematical Analysis ; 12 (2018), 3. - pp. 515-540. - eISSN 1735-8787 |
URL of original publication: | https://projecteuclid.org/euclid.bjma/1510909221, Last access on Aug 7, 2018 |
DOI (citable link): | https://dx.doi.org/10.1215/17358787-2017-0024 |
Summary: |
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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Subject (DDC): | 510 Mathematics |
Bibliography of Konstanz: | Yes |
Refereed: | Yes |
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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. 12(3), pp. 515-540. eISSN 1735-8787. Available under: doi: 10.1215/17358787-2017-0024
@article{Denk2018Kolmo-32428.3, title={Kolmogorov-type and general extension results for nonlinear expectations}, url={https://projecteuclid.org/euclid.bjma/1510909221}, year={2018}, doi={10.1215/17358787-2017-0024}, 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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