A random Euler scheme for Carathéodory differential equations

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摘要

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.

论文关键词：Carathéodory differential equations,Euler scheme,Monte–Carlo methods

论文评审过程：Received 1 October 2007, Revised 26 February 2008, Available online 27 June 2008.

论文官网地址：https://doi.org/10.1016/j.cam.2008.05.060