The multi-level Monte Carlo approach is a powerful variance reduction technique, which is applied, in particular, in the context of SDEs. While the standard task is to compute the expectation of a real-valued functional, we discuss how to approximate a distribution function on a compact interval in this talk. We establish upper bounds for the error of suitable multi-level algorithms. Moreover, we brieﬂy discuss an application to asymmetric ﬂow ﬁeld ﬂow fractionation (AF4 ), which involves exit times of reﬂected diﬀusions. Joint work with Mike Giles (Oxford Univ.), Oleg Iliev (Fraunhofer ITWM, Kaiserslautern), and Tigran Nagapetyan (Fraunhofer ITWM, Kaiserslautern). Supported by the DFG within Priority Program 1324.
Klaus Ritter received his Diploma, PhD, and the venia legendi at the Department of Mathematics, Universitat Erlangen-Nurnberg,in the years 1988, 1990, and 1996, respectively. He joined the Department of Mathematics and Computer Science, Universitat Passau, as a senior scientific assistant in 1998. During the 1990th he also spend one year at the Department of Computer Science, University of Kentucky, Lexington, and half a year at the Department of Computer Science and the Lamont Doherty Earth Observatory, Columbia University, New York. In 2000 he became Professor at the Department of Mathematics, Technische Universitat Darmstadt. Since 2010 Klaus Ritter is chairing the research group on Computational Stochastics at the Department of Mathematics, Technische Universitat Kaiserslautern. His research is focused on numerics of stochastic (partial) differential equations, infinite dimensional integration, complexity of continuous problems, and Monte Carlo algorithms. Applications in engineering, finance, and commerce are addressed in joint projects at the Fraunhofer Institute for Industrial Mathematics (ITWM) and the Center for Mathematical and Computational Modeling (CM^2) in Kaiserslautern and in cooperations with well-known industrial partners.