A semigroup approach to nonlinear Lévy processes
| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Denk, Robert; Kupper, Michael; Nendel, Max |
| Year of publication: | 2020 |
| Published in: | Stochastic Processes and their Applications ; 130 (2020), 3. - pp. 1616-1642. - Elsevier. - ISSN 0304-4149. - eISSN 1879-209X |
| ArXiv-ID: | arXiv:1710.08130 |
| DOI (citable link): | https://dx.doi.org/10.1016/j.spa.2019.05.009 |
| Summary: |
We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators (Aλ)λ∈Λ of linear Lévy processes which guarantees the existence of a nonlinear Lévy process such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE ∂tu=supλ∈ΛAλu . The results are illustrated with several examples.
|
| MSC Classification: | 60G51, 49L25, 47H20 |
| Subject (DDC): | 510 Mathematics |
| Keywords: | Lévy process; Convex expectation space; Markovian convolution semigroup; Fully nonlinear PDE; Nisio semigroup |
| Bibliography of Konstanz: | Yes |
| Refereed: | Yes |
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DENK, Robert, Michael KUPPER, Max NENDEL, 2020. A semigroup approach to nonlinear Lévy processes. In: Stochastic Processes and their Applications. Elsevier. 130(3), pp. 1616-1642. ISSN 0304-4149. eISSN 1879-209X. Available under: doi: 10.1016/j.spa.2019.05.009
@article{Denk2020semig-40474.2, title={A semigroup approach to nonlinear Lévy processes}, year={2020}, doi={10.1016/j.spa.2019.05.009}, number={3}, volume={130}, issn={0304-4149}, journal={Stochastic Processes and their Applications}, pages={1616--1642}, author={Denk, Robert and Kupper, Michael and Nendel, Max} }
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