Publikation: A semigroup approach to nonlinear Lévy processes
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2020
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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
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Lévy process; Convex expectation space; Markovian convolution semigroup; Fully nonlinear PDE; Nisio semigroup
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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. 2020, 130(3), pp. 1616-1642. ISSN 0304-4149. eISSN 1879-209X. Available under: doi: 10.1016/j.spa.2019.05.009BibTex
@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} }
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