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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 194341, 10 pages
http://dx.doi.org/10.1155/2014/194341
Research Article

Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

1School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
2Institute for Financial Studies and School of Mathematics, Shandong University, Jinan 250199, China

Received 12 December 2013; Accepted 27 January 2014; Published 24 March 2014

Academic Editor: Litan Yan

Copyright © 2014 Qingfeng Zhu and Yufeng Shi. 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

Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.