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Journal of Applied Mathematics
Volume 2012, Article ID 582645, 17 pages
http://dx.doi.org/10.1155/2012/582645
Research Article

Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

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 12 May 2012; Accepted 26 November 2012

Academic Editor: Shiping Lu

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

We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.