On existence and uniqueness properties for solutions of stochastic fixed point equations
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2021-09
Publication Type
Journal Article
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Abstract
The Feynman–Kac formula implies that every suitable classical solution of a semilinear Kolmogorov partial differential equation (PDE) is also a solution of a certain stochastic fixed point equation (SFPE). In this article we study such and related SFPEs. In particular, the main result of this work proves existence of unique solutions of certain SFPEs in a general setting. As an application of this main result we establish the existence of unique solutions of SFPEs associated with semilinear Kolmogorov PDEs with Lipschitz continuous nonlinearities even in the case where the associated semilinear Kolmogorov PDE does not possess a classical solution.
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published
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26 (9)
Pages / Article No.
4927 - 4962
Publisher
American Institute of Mathematical Sciences
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Subject
Stochastic analysis; Stochastic fixed point equations; Stochastic differential equations; Kolmogorov partial differential equations; Multilevel Picard approximations; Feynman–Kac formula
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03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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Is new version of: http://hdl.handle.net/20.500.11850/452452