Katharina Klioba (TU Hamburg): Discretising SPDEs in Time: How to obtain Pathwise Uniform Convergence Rates

Abstract:

In this talk, I will present optimal bounds for the pathwise uniform strong error arising from temporal discretisation of semi-linear stochastic evolution equations. Up to a logarithmic factor, we recover the convergence rates for the whole path from the linear PDE which corresponds to the semi-linear SPDE with globally Lipschitz nonlinearity and noise. This extends and improves previous results from splitting to general time discretisation schemes and from the group to the semigroup case. We illustrate how novel maximal inequalities for stochastic convolutions were used to obtain these results, which are applicable to a large class of hyperbolic equations. As an example, we discuss the convergence rates of implicit Euler and splitting for the nonlinear Schrödinger equation with  multiplicative noise.
This talk is based on joint work with Mark Veraar (TU Delft).

Zoom Link:
https://uni-kassel.zoom.us/j/96217091997?pwd=RVRaVVBRclFJYU9jczNZSWF3SXI2QT09

Meeting ID: 962 1709 1997
Passcode: cauchy