Wednesday, May 21, 2025 - 14:30 in V2-210
Optimal convergence rates in time for hyperbolic SPDEs: A unified approach
A talk in the SPDEvent series by
Katharina Klioba from Delft University of Technology
| Abstract: |
In this talk, optimal bounds are presented for the pathwise uniform error arising from temporal discretisation of semi-linear SPDEs with Gaussian noise. The focus lies on hyperbolic equations with globally Lipschitz nonlinearities, including Schrödinger, Maxwell’s, and wave equations, which are treated within a unified abstract framework. We recover the deterministic convergence rates up to order ½ for multiplicative noise and up to order 1 for wave equations or additive noise up to a logarithmic factor. Via novel path regularity results, we show that these are indeed optimal on the full time interval. This extends and improves previous results from exponential Euler to general contractive time discretisation schemes, such as implicit Euler, and from the group to the semigroup case. As an outlook, we discuss how the approach may extend to polynomially growing nonlinearities.
This talk is based on joint work with Mark Veraar (Delft University of Technology).
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