Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 275747, 15 pages
Weak Approximation of SDEs by Discrete-Time Processes
Faculty of Mathematics, Dortmund University of Technology, Vogelpothsweg 87, 44227 Dortmund, Germany
Received 29 October 2007; Revised 25 January 2008; Accepted 20 February 2008
Academic Editor: Nikolai Leonenko
Copyright © 2008 Henryk Zähle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.