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Journal of Function Spaces
Volume 2016 (2016), Article ID 5916132, 9 pages
http://dx.doi.org/10.1155/2016/5916132
Research Article

SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions

School of Mathematics and Statistics, Suzhou University, Anhui 234000, China

Received 30 March 2016; Accepted 30 June 2016

Academic Editor: Gianluca Vinti

Copyright © 2016 Pengju Duan. 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

The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate.