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July 2018 Kolmogorov-type and general extension results for nonlinear expectations
Robert Denk, Michael Kupper, Max Nendel
Banach J. Math. Anal. 12(3): 515-540 (July 2018). DOI: 10.1215/17358787-2017-0024

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 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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Robert Denk. Michael Kupper. Max Nendel. "Kolmogorov-type and general extension results for nonlinear expectations." Banach J. Math. Anal. 12 (3) 515 - 540, July 2018. https://doi.org/10.1215/17358787-2017-0024

Information

Received: 21 February 2017; Accepted: 19 June 2017; Published: July 2018
First available in Project Euclid: 17 November 2017

zbMATH: 06946069
MathSciNet: MR3824739
Digital Object Identifier: 10.1215/17358787-2017-0024

Subjects:
Primary: 28C05
Secondary: 28A12, 46A20, 46A55, 47H07

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 3 • July 2018
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