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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 technique is uncertainty quan-tification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the… (More)

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 MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment… (More)

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607–617] proposed and analyzed an MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a single level… (More)

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