Randomised one-step time integration methods for deterministic operator differential equations
- Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al. (Stat Comput 27(4):1065-1082, 2017) proposed randomisation of deterministic time integration methods as a strategy for quantifying uncertainty due to the unknown time discretisation error. We consider this strategy for systems that are described by deterministic, possibly time-dependent operator differential equations defined on a Banach space or a Gelfand triple. Our main results are strong error bounds on the random trajectories measured in Orlicz norms, proven under a weaker assumption on the local truncation error of the underlying deterministic time integration method. Our analysis establishes the theoretical validity of randomised time integration for differential equations in infinite-dimensional settings.
Author details: | Han Cheng LieORCiD, Martin StahnORCiDGND, Tim J. SullivanORCiDGND |
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DOI: | https://doi.org/10.1007/s10092-022-00457-6 |
ISSN: | 0008-0624 |
ISSN: | 1126-5434 |
Title of parent work (English): | Calcolo |
Publisher: | Springer |
Place of publishing: | Milano |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/02/25 |
Publication year: | 2022 |
Release date: | 2023/12/14 |
Tag: | Operator differential equations; Randomisation; Time integration; Uncertainty quantification |
Volume: | 59 |
Issue: | 1 |
Article number: | 13 |
Number of pages: | 33 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [318763901-SFB1294] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |