Journal of Applied Mathematics
Volume 2012 (2012), Article ID 304781, 14 pages
http://dx.doi.org/10.1155/2012/304781
Research Article

Comparison Theorems for the Multidimensional BDSDEs and Applications

Bo Zhu1 and Baoyan Han2

1School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
2Shandong University of Art and Design, Jinan 250014, China

Received 16 December 2011; Accepted 16 February 2012

Academic Editor: A. A. Soliman

Copyright © 2012 Bo Zhu and Baoyan Han. 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.

Abstract

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.