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Article
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stoch...
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Article
Analysis of Discrete \(L^2\) Projection on Polynomial Spaces with Random Evaluations
We analyze 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 te...
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Article
Monte Carlo Euler approximations of HJM term structure financial models
We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional space...
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Article
Convergence Rates for an Adaptive Dual Weighted Residual Finite Element Algorithm
Basic convergence rates are established for an adaptive algorithm based on the dual weighted residual error representation, $$\mbox{er...
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Article
Worst case scenario analysis for elliptic problems with uncertainty
This work studies linear elliptic problems under uncertainty. The major emphasis is on the deterministic treatment of such uncertainty. In particular, this work uses the Worst Scenario approach for the charact...