Title: Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations,
Abstract: Although for a number of semilinear stochastic wave equations existence and
uniqueness results for corresponding solution processes are known from the
literature, these solution processes are typically not explicitly known and
numerical approximation methods are needed in order for mathematical modelling
with stochastic wave equations to become relevant for real world applications.
This, in turn, requires the numerical analysis of convergence rates for such
numerical approximation processes. A recent article by the authors proves upper
bounds for weak errors for spatial spectral Galerkin approximations of a class
of semilinear stochastic wave equations. The findings there are complemented by
the main result of this work, that provides lower bounds for weak errors which
show that in the general framework considered the established upper bounds can
essentially not be improved.