Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 275747, 15 pages
doi:10.1155/2008/275747
Abstract
We 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.