On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion

2015/10/07 by Helmut Harbrecht, Michael Peters, Markus Siebenmorgen · 3 citations
Mathematics · Decision Sciences · Economics, Econometrics and Finance · #Mathematical Approximation and Integration #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications

paper · doi:10.1090/mcom/3107

Abstract

This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. In particular, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings.

Citations

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