A semigroup approach to nonlinear Lévy processes
| dc.contributor.author | Denk, Robert | |
| dc.contributor.author | Kupper, Michael | |
| dc.contributor.author | Nendel, Max | |
| dc.date.accessioned | 2020-09-11T11:37:11Z | |
| dc.date.available | 2020-09-11T11:37:11Z | |
| dc.date.issued | 2020 | eng |
| dc.description.abstract | 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. | eng |
| dc.description.version | published | eng |
| dc.identifier.arxiv | 1710.08130 | eng |
| dc.identifier.doi | 10.1016/j.spa.2019.05.009 | eng |
| dc.identifier.ppn | 494964324 | |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/40474.2 | |
| dc.language.iso | eng | eng |
| dc.rights | terms-of-use | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject | Lévy process; Convex expectation space; Markovian convolution semigroup; Fully nonlinear PDE; Nisio semigroup | eng |
| dc.subject.ddc | 510 | eng |
| dc.subject.msc | 60G51, 49L25, 47H20 | |
| dc.title | A semigroup approach to nonlinear Lévy processes | eng |
| dc.type | JOURNAL_ARTICLE | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @article{Denk2020semig-40474.2,
year={2020},
doi={10.1016/j.spa.2019.05.009},
title={A semigroup approach to nonlinear Lévy processes},
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}
} | |
| kops.citation.iso690 | DENK, Robert, Michael KUPPER, Max NENDEL, 2020. A semigroup approach to nonlinear Lévy processes. In: Stochastic Processes and their Applications. Elsevier. 2020, 130(3), pp. 1616-1642. ISSN 0304-4149. eISSN 1879-209X. Available under: doi: 10.1016/j.spa.2019.05.009 | deu |
| kops.citation.iso690 | DENK, Robert, Michael KUPPER, Max NENDEL, 2020. A semigroup approach to nonlinear Lévy processes. In: Stochastic Processes and their Applications. Elsevier. 2020, 130(3), pp. 1616-1642. ISSN 0304-4149. eISSN 1879-209X. Available under: doi: 10.1016/j.spa.2019.05.009 | eng |
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| kops.sourcefield | Stochastic Processes and their Applications. Elsevier. 2020, <b>130</b>(3), pp. 1616-1642. ISSN 0304-4149. eISSN 1879-209X. Available under: doi: 10.1016/j.spa.2019.05.009 | deu |
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