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Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005505
URN to cite this document: urn:nbn:de:bvb:703-epub-5505-2

Title data

Grüne, Lars:
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation.
Bayreuth , 2003

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Abstract

Generalizing an idea from deterministic optimal control, we construct a posteriori error estimates for the spatial discretization error of the stochastic dynamic programming method based on a discrete Hamilton-Jacobi-Bellman equation. These error estimates are shown to be efficient and reliable, furthermore, a priori bounds on the estimates depending on the regularity of the approximate solution are derived. Based on these error estimates we propose an adaptive space discretization scheme whose performance is illustrated by two numerical examples.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Erscheint in: Numerische Mathematik. Bd. 99 (2004) Heft 1 . - S. 85-112; https://doi.org/10.1007/s00211-004-0555-4
Keywords: Stochastic optimal control; Stochastic Hamilton-Jacobi-Bellmanequation; Posteriori error estimates; Feedback optimal control; Numerical examples
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5505-2
Date Deposited: 12 May 2021 13:30
Last Modified: 21 Jun 2021 08:40
URI: https://epub.uni-bayreuth.de/id/eprint/5505

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