Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Spectral methods in MatLab
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
An Efficient Monte Carlo Method for Optimal Control Problems with Uncertainty
Computational Optimization and Applications
Stochastic Computational Fluid Mechanics
Computing in Science and Engineering
An efficient sampling method for stochastic inverse problems
Computational Optimization and Applications
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
A variance reduction method based on sensitivity derivatives
Applied Numerical Mathematics
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A previous paper introduced a sampling method (SDES) based on sensitivity derivatives to construct statistical moment estimates that are more efficient than standard Monte Carlo estimates. In this paper we sharpen previous theoretical results and introduce a criterion to guarantee that the variance of SDES estimates is smaller than the variance of the Monte Carlo estimate. Previous numerical experiments demonstrated, and here we prove analytically, that the first-order SDES and Monte Carlo estimates converge at the same rate. We illustrate the efficiency of the SDES method of order n, where n is fixed, to estimate statistical moments with a Korteweg-de Vries equation with uncertain initial conditions.