Ekvationer
Seminarium i matematik

Optimal Pathwise Uniform Convergence Rates of Time Discretisation Schemes for SPDEs

Välkommen till föreläsningen i seminarieserien i matematik.

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 semigroup corresponding to the semi-linear SPDE with globally Lipschitz nonlinearity and noise. This extends and improves previous results from exponential Euler to general contractive 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 and exponential Euler for the nonlinear Schrödinger equation with multiplicative noise.

 

This talk is based on joint work with Mark Veraar (TU Delft).

B1009 Katharina Klioba, TU Hamburg-Harburg, Germany Lägg till i din kalender