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A random Euler scheme for Carathéodory differential equations

2008; Elsevier BV; Volume: 224; Issue: 1 Linguagem: Inglês

10.1016/j.cam.2008.05.060

1879-1778

Arnulf Jentzen, Andreas Neuenkirch,

Mathematical functions and polynomials

We study a random Euler scheme for the approximation of Carathéodory 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.