Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

The reduced basis method was introduced for the accurate online evaluation of solutions to
a parameter dependent family of elliptic PDEs. Abstractly, it can be viewed as determining a …

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random
coefficients. We focus on models of the random coefficient that lack uniform ellipticity and …

For a function g (h), we write g (h)= O (hp) to mean that there exist constants h0> 0 and K> 0
(independent of h) such that| g (h)|< Khp for all| h|< h0. In words, this means that g (h) tends …

In this article, we study the approximation of a probability measure μ on Rd by its empirical
measure ˆμN interpreted as a random quantization. As error criterion we consider an …

In this paper, we propose a method for the numerical solution of linear systems of equations
in low rank tensor format. Such systems may arise from the discretisation of PDEs in high …

This book is an extended written version of the Master 2 course “Probabilités
Numériques”(ie, Numerical Probability or Numerical Methods in Probability) which has been …

Stochastic collocation methods for approximating the solution of partial differential equations
with random input data (eg, coefficients and forcing terms) suffer from the curse of …

In this paper we propose and analyze stable variational formulations for convection diffusion
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …

Der Text gibt eine Einführung in die Mathematik und die Anwendungsmöglichkeiten der
Monte Carlo-Methoden und verwendet dazu durchgängig die Sprache der Stochastik. Der …