A semigroup approach to nonlinear Levy processes

Denk R, Kupper M, Nendel M (2020)
Stochastic Processes and their Applications 130(3): 1616-1642.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Denk, Robert; Kupper, Michael; Nendel, MaxUniBi
Abstract / Bemerkung
We study the relation between Levy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Levy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators (A(lambda))(lambda is an element of Lambda) of linear Levy processes which guarantees the existence of a nonlinear Levy process such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE partial derivative(t)u = sup(lambda is an element of Lambda) A(lambda)u. The results are illustrated with several examples. (C) 2019 Published by Elsevier B.V.
Stichworte
Levy process; Convex expectation space; Markovian convolution semigroup; Fully nonlinear PDE; Nisio semigroup
Erscheinungsjahr
2020
Zeitschriftentitel
Stochastic Processes and their Applications
Band
130
Ausgabe
3
Seite(n)
1616-1642
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2941873

Zitieren

Denk R, Kupper M, Nendel M. A semigroup approach to nonlinear Levy processes. Stochastic Processes and their Applications. 2020;130(3):1616-1642.
Denk, R., Kupper, M., & Nendel, M. (2020). A semigroup approach to nonlinear Levy processes. Stochastic Processes and their Applications, 130(3), 1616-1642. https://doi.org/10.1016/j.spa.2019.05.009
Denk, R., Kupper, M., and Nendel, M. (2020). A semigroup approach to nonlinear Levy processes. Stochastic Processes and their Applications 130, 1616-1642.
Denk, R., Kupper, M., & Nendel, M., 2020. A semigroup approach to nonlinear Levy processes. Stochastic Processes and their Applications, 130(3), p 1616-1642.
R. Denk, M. Kupper, and M. Nendel, “A semigroup approach to nonlinear Levy processes”, Stochastic Processes and their Applications, vol. 130, 2020, pp. 1616-1642.
Denk, R., Kupper, M., Nendel, M.: A semigroup approach to nonlinear Levy processes. Stochastic Processes and their Applications. 130, 1616-1642 (2020).
Denk, Robert, Kupper, Michael, and Nendel, Max. “A semigroup approach to nonlinear Levy processes”. Stochastic Processes and their Applications 130.3 (2020): 1616-1642.

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