We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders andâ€¦ (More)

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by randomâ€¦ (More)

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to ItÃ´ stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607â€“617] proposed andâ€¦ (More)

Abstract. In this work we consider the random discrete L2 projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of aâ€¦ (More)

We analyse 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 possibleâ€¦ (More)

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 adaptiveâ€¦ (More)

Abstract. The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of theâ€¦ (More)

This work is concentrated on efforts to efficiently compute properties of systems, modelled by differential equations, involving multiple scales. Goal oriented adaptivity is the common approach toâ€¦ (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 MCâ€¦ (More)