Uncertainty quantification (UQ) includes the characterization, integration, and propagation of
uncertainties that result from stochastic variations and a lack of knowledge or data in the …

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

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

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 …

In this paper, we establish that for a wide class of controlled stochastic differential equations
(SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be …

In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-
dimensional SDEs driven by Brownian motions. Giles has previously shown that if we …

Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has
been rapid development of the technique for a variety of applications in computational …