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A continuation multilevel Monte Carlo algorithm
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 ofExpand
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  • Open Access
Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete L2 Projection on Polynomial Spaces
tl;dr
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. Expand
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  • Open Access
Adaptive Multilevel Monte Carlo Simulation
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values dependingExpand
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Implementation and analysis of an adaptive multilevel Monte Carlo algorithm
tl;dr
We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximation of solutions to Itô stochastic differential equations (SDE). Expand
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  • Open Access
Adaptive Monte Carlo Algorithms for Stopped Diffusion
We present adaptive algorithms for weak approximation of stopped diffusion using the Monte Carlo Euler method. The goal is to compute an expected value E[g(X(τ), τ)] of a given function g dependingExpand
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Analysis of Discrete $$L^2$$L2 Projection on Polynomial Spaces with Random Evaluations
tl;dr
We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. Expand
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  • Open Access
On NonAsymptotic Optimal Stopping Criteria in Monte Carlo Simulations
tl;dr
We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. Expand
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An Adaptive Algorithm for Ordinary, Stochastic and Partial Differential Equations
The theory of a posteriori error estimates suitable for adaptive refinement is well established. This work focuses on the fundamental, but less studied, issue of convergence rates of adaptive algorExpand
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  • Open Access
ON NON-ASYMPTOTIC OPTIMAL STOPPING CRITERIA IN MONTE CARLO SIMULATIONS
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 MCExpand
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  • Open Access