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Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations

Annika Lang (Institutionen för matematiska vetenskaper, matematisk statistik) ; Andreas Petersson (Institutionen för matematiska vetenskaper, matematisk statistik)

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.

Nyckelord: stochastic partial differential equations, weak convergence, (multilevel) Monte Carlo methods, upper and lower error bounds

Denna post skapades 2015-12-16. Senast ändrad 2015-12-17.
CPL Pubid: 228542


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)


Sannolikhetsteori och statistik

Chalmers infrastruktur

C3SE/SNIC (Chalmers Centre for Computational Science and Engineering)