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 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 …

For a function g (h), we write g (h)= O (hp) to mean that there exist constants h0> 0 and K> 0
(independent of h) such that| g (h)|< Khp for all| h|< h0. In words, this means that g (h) tends …

This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of
the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and …

The use of computational models and simulations to predict events that take place in our
physical universe, or to predict the behaviour of engineered systems, has significantly …

We introduce a class of adaptive time-stepping strategies for stochastic differential equations
with non-Lipschitz drift coefficients. These strategies work by controlling potential …

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

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

We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to
the class of density-driven flow problems, in particular the problem of salinisation of coastal …

Multifidelity methods leverage low-cost surrogate models to speed up computations and
make occasional recourse to expensive high-fidelity models to establish accuracy …