Publications by Erik Gustaf Bogislaw Von Schwerin

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and ...

2016

A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolera ...

2015

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The CMLMC algorithm so ...

MATHICSE2014

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. Moreover, we discuss extensions to non-unif ...

MATHICSE2014

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Erik Gustaf Bogislaw Von Schwerin, Hakon Andreas Hoel

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both b ...

Siam Publications2014

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

MATHICSE2011

Erik Gustaf Bogislaw Von Schwerin

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Optimization of mesh hierarchies in multilevel Monte Carlo samplers

A continuation multilevel Monte Carlo algorithm

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

A continuation multilevel Monte Carlo algorithm

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers