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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 827192, 11 pages
http://dx.doi.org/10.1155/2013/827192
Research Article

The -Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs

1College of Information Science and Technology, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China
2School of Sciences, Ningbo University of Technology, 201 Fenghua Road, Ningbo 315211, China
3Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China

Received 28 May 2013; Revised 7 June 2013; Accepted 8 June 2013

Academic Editor: Ming Li

Copyright © 2013 Zhi Wang and Litan Yan. 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

Let be a subfractional Brownian motion with index . Based on the -transform in white noise analysis we study the stochastic integral with respect to , and we also prove a Girsanov theorem and derive an Itô formula. As an application we study the solutions of backward stochastic differential equations driven by of the form , where the stochastic integral used in the above equation is Pettis integral. We obtain the explicit solutions of this class of equations under suitable assumptions.