TY  - JOUR
A1  - Lie, Han Cheng
A1  - Stahn, Martin
A1  - Sullivan, Tim J.
T1  - Randomised one-step time integration methods for deterministic operator differential equations
T2  - Calcolo
N2  - 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.
KW  - Time integration
KW  - Operator differential equations
KW  - Randomisation
KW  - Uncertainty quantification
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/61873
SN  - 0008-0624
SN  - 1126-5434
VL  - 59
IS  - 1
PB  - Springer
CY  - Milano
ER  -