A random Euler scheme for Carathéodory differential equations

Authors:
A. Jentzen;A. Neuenkirch
Affiliations:
Johann Wolfgang Goethe-Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Street 6-10, D-60325 Frankfurt am Main, Germany;Johann Wolfgang Goethe-Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Street 6-10, D-60325 Frankfurt am Main, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We study a random Euler scheme for the approximation of Caratheodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte-Carlo method for integration problems.