On existence and uniqueness properties for solutions of stochastic fixed point equations


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Date

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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Volume

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

Organisational unit

03874 - Hungerbühler, Norbert / Hungerbühler, Norbert check_circle
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics check_circle

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