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03/07/2023
Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems
We develop new multilevel Monte Carlo (MLMC) methods to estimate the exp...
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12/22/2022
Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation
In this paper we propose and analyse a method for estimating three quant...
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12/22/2021
Preintegration is not smoothing when monotonicity fails
Preintegration is a technique for high-dimensional integration over d-di...
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12/20/2021
Approximating distribution functions and densities using quasi-Monte Carlo methods after smoothing by preintegration
The cumulative distribution or probability density of a random variable,...
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03/30/2021
Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on ℝ^d
We prove that a variant of the classical Sobolev space of first-order do...
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03/05/2021
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: Efficient algorithms and numerical results
Stochastic PDE eigenvalue problems often arise in the field of uncertain...
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10/02/2020
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: Regularity and error analysis
Random eigenvalue problems are useful models for quantifying the uncerta...
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12/19/2017
Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals
In this paper we focus on efficient implementations of the Multivariate ...
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03/02/2017