Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random
coefficients. We focus on models of the random coefficient that lack uniform ellipticity and …

We propose and analyze a novel multi-index Monte Carlo (MIMC) method for weak
approximation of stochastic models that are described in terms of differential equations …

Stochastic collocation methods for approximating the solution of partial differential equations
with random input data (eg, coefficients and forcing terms) suffer from the curse of …

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak
approximation of stochastic models. The CMLMC algorithm solves the given approximation …

Multilevel Monte Carlo (MLMC) and recently proposed unbiased estimators are closely
related. This connection is elaborated by presenting a new general class of unbiased …

We study the strong approximation of stochastic differential equations with discontinuous
drift coefficients and (possibly) degenerate diffusion coefficients. To account for the …

We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC)
discretization hierarchy based on uniform discretization methods with general approximation …

Multifidelity Monte Carlo (MFMC) estimation combines low-and high-fidelity models to speed
up the estimation of statistics of the high-fidelity model outputs. MFMC optimally samples the …

In this study, we present an adaptive multilevel Monte Carlo (AMLMC) algorithm for
approximating deterministic, real-valued, bounded linear functionals that depend on the …