@article{LieStahnSullivan2022,
  author    = {Lie, Han Cheng and Stahn, Martin and Sullivan, Tim J.},
  title     = {Randomised one-step time integration methods for deterministic operator differential equations},
  series = {Calcolo},
  volume    = {59},
  journal   = {Calcolo},
  number    = {1},
  publisher = {Springer},
  address   = {Milano},
  issn      = {0008-0624},
  doi       = {10.1007/s10092-022-00457-6},
  pages     = {33},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}