Zähle, Henryk2008-04-152008-04-152008-04-15http://hdl.handle.net/2003/2518610.17877/DE290R-69We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.enMathematical Preprints;2008-01stochastic differential equationmartingale problemDoob-Meyer decompositiondiscrete-time processweak convergenceGalton-Watson processEuler scheme510preprint