Multilevel Monte-Carlo Methods for SPDEs
We study infinite-dimensional integration wrt
the distribution of the mild solution $X$ of
an spde at the final time point $T$,
i.e. computation of the expected value
$E(f(X(T)))$ for certain functionals $f$. In this
talk we focus on Lipschitz functionals and we
combine the multi-level technique with
results for pathwise approximation of $X$ to
obtain new algorithms and corresponding error
bounds for the integration problem.
The theoretical analysis is complemented by
numerical experiments. \\
This is a joint work with Simone Graubner and
Klaus Ritter (TU Darmstadt).