# Seminar

## Quantification of Uncertainty via Multilevel Monte Carlo Methods

### Thursday, May 18, 2017 5:15 PM;

JGU Mainz, Mathematics, Hilbert-Raum

Speaker: Andrea Barth; Universität Stuttgart

Multilevel Monte Carlo methods were introduced to decrease the computational complexity
of the calculation of, for instance, the expectation of a random quantity. More
precisely, in comparison to standard Monte Carlo methods, the computational complexity
is (asymptotically) equal to the calculation of one sample of the problem on the
finest discretization grid used. The price to pay for this increase in efficiency is that
the problem must be solved not only on one (fine) grid, but on a hierarchy of discretizations.
This implies, first, that the solution has to be represented on all grids and,
second, that the variance of the detail (the difference of approximate solutions on two
consecutive grids) converges with the refinement of the grid.
In this talk, I will give an introduction to multilevel Monte Carlo methods in the case
when the variance of the detail does not converge uniformly. The idea is illustrated by
the calculation of the expectation for an elliptic problem with a random (multiscale)
coefficient and then extended to approximations of discontinous nature, e.g. Poisson
noise.

## Calendar

## Contact

- Scientific Coordinator of the TRR 146
- Dr. Giovanni Settanni
- Staudingerweg 9
- D-55128 Mainz
- trr146aUVZW@.Hjmiiwuni-mainz.de