Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations
Preprint, 2015

The simulation of weak error rates for the stochastic heat equation driven by multiplicative noise is presented. It is shown why conventional Monte Carlo approximations fail for these computationally expensive problems with small errors, and two different estimators for the weak error are presented that perform better in theory and in practice. One is another Monte Carlo estimator while the other one includes a multilevel Monte Carlo approximation in the computation of error plots.

upper and lower error bounds

stochastic partial differential equations

(multilevel) Monte Carlo methods

weak convergence


Annika Lang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Andreas Petersson

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet



Sannolikhetsteori och statistik


Grundläggande vetenskaper


C3SE (Chalmers Centre for Computational Science and Engineering)