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Your search keyword '"Markovian convolution semigroup"' showing total 2 results
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2 results on '"Markovian convolution semigroup"'

1. A semigroup approach to nonlinear Lévy processes.

Author

Denk, Robert, Kupper, Michael, and Nendel, Max

Subjects
*LEVY processes, *VISCOSITY solutions
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 (A λ) 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 ∂ t u = sup λ ∈ Λ A λ u. The results are illustrated with several examples. [ABSTRACT FROM AUTHOR]

Published
2020
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2. A Semigroup Approach to Nonlinear Lévy Processes

Author

Max Nendel, Michael Kupper, and Robert Denk

Subjects
Statistics and Probability, Pure mathematics, L25, Infinitesimal, Markov process, 01 natural sciences, Lévy process, fully nonlinear PDE, Convolution, 010104 statistics & probability, symbols.namesake, ddc:330, Nisio semigroup, 0101 mathematics, Levy process, G51, Mathematics, Semigroup, Applied Mathematics, 010102 general mathematics, Nonlinear system, Modeling and Simulation, Markovian convolution semigroup, symbols, H20, Viscosity solution, convex expectation space
Abstract

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.

Published
2019

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