Artificial neural networks (ANNs) have very successfully been used in numerical simulations
for a series of computational problems ranging from image classification/image recognition …

This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

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

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of
a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided …

This is the second volume of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems. The second volume deals with algorithms using …

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing
nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the …

For a long time it has been well-known that high-dimensional linear parabolic partial
differential equations (PDEs) can be approximated by Monte Carlo methods with a …

We present some results on the complexity of numerical integration. We start with the
seminal paper of Bakhvalov (1959) and end with new results on the curse of dimensionality …

Der Text gibt eine Einführung in die Mathematik und die Anwendungsmöglichkeiten der
Monte Carlo-Methoden und verwendet dazu durchgängig die Sprache der Stochastik. Der …